From 387636720a9ac44a16536e56693960e79711b642 Mon Sep 17 00:00:00 2001 From: ComFreek Date: Wed, 5 Aug 2020 19:07:37 +0200 Subject: [PATCH 01/28] detail tbox/abox difference partially copied verbatim from https://en.wikipedia.org/w/index.php?title=Abox&oldid=892872890, ideally later cite as described on https://en.wikipedia.org/w/index.php?title=Special:CiteThisPage&page=Abox&id=892872890&wpFormIdentifier=titleform --- WuV/onto_general.tex | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/WuV/onto_general.tex b/WuV/onto_general.tex index 28b5d83..872531b 100644 --- a/WuV/onto_general.tex +++ b/WuV/onto_general.tex @@ -71,6 +71,15 @@ \section{General Principles}\label{sec:onto:principles} This part is commonly called the \textbf{ABox} (A for assertional). \end{compactitem} +TBox declarations tend to be more permanent within a knowledge base and are used as a schema. +In contrast, ABox declarations are much more dynamic in nature and tend to represent instance data. +For instance, we can understand relational databases as ontologies made up of table definitions as TBox declarations and table rows as ABox declarations. +There, both kind of declarations are even separately stored for efficiency reasons, and in particular, the concrete way of representing table rows +as bits is determined by the corresponding table definitions. +However, such a hard distinction is not necessarily the case for other ontology languages. +For example, in the ontology language OWL or in general in triplestores, both kind of declarations are stored next to each other and the syntactic representation distinction blurs. +Nonetheless, we can usually distinguish between both declarations by their usage and lifecycle during the development of a concrete ontology. + A separate division into two parts is the following: \begin{compactitem} \item The \textbf{signature} part contains everything that introduces a \textbf{named entity}: individuals, concepts, relations, and properties. From b884df7f42efba0b86886ef37720f8a879b31815 Mon Sep 17 00:00:00 2001 From: ComFreek Date: Thu, 6 Aug 2020 12:40:44 +0200 Subject: [PATCH 02/28] BOL semantics: add missing refl axiom to for R* --- WuV/bolsem.tex | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/WuV/bolsem.tex b/WuV/bolsem.tex index e11df03..5024c63 100644 --- a/WuV/bolsem.tex +++ b/WuV/bolsem.tex @@ -144,6 +144,7 @@ \subsection{Semantics} \begin{compactitem} \item A binary predicate symbol $C_R\sq i\times i$. Note that $R$ may be a complex expression; so we have to generate a fresh name $C_R$ here. \item The axiom $\forall x:\iota,y:\iota.\,R(x,y)\impl C_R(x,y)$, i.e., $C_R$ extends $R$. + \item The axiom $\forall x:\iota.\,C_R(x,x)$, i.e., $C_R$ is reflexive \item The axiom $\forall x:\iota,y:\iota,z:\iota.\,C_R(x,y)\wedge C_R(y,z)\impl C_R(x,z)$, i.e., $C_R$ is transitive. \end{compactitem} \item We add the case $\sem{R^*}=C_R(x,y)$ to the interpretation function. @@ -625,4 +626,4 @@ \section{Exercise 2} You have to implement that as well or use a library for it. We recommend not focusing on implementing the syntax and semantics in their entirety. -It is more instructive to save time by choosing a sublanguage of BOL (by omitting some productions) and to use the time to implement a second semantics. \ No newline at end of file +It is more instructive to save time by choosing a sublanguage of BOL (by omitting some productions) and to use the time to implement a second semantics. From e4934ba71a850ee90c895e7fd03d0905ef765ab0 Mon Sep 17 00:00:00 2001 From: ComFreek Date: Thu, 6 Aug 2020 12:41:20 +0200 Subject: [PATCH 03/28] BOL semantics: add missing refl axiom for C_R* --- WuV/bolsem.tex | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/WuV/bolsem.tex b/WuV/bolsem.tex index e11df03..74b9a4c 100644 --- a/WuV/bolsem.tex +++ b/WuV/bolsem.tex @@ -144,6 +144,7 @@ \subsection{Semantics} \begin{compactitem} \item A binary predicate symbol $C_R\sq i\times i$. Note that $R$ may be a complex expression; so we have to generate a fresh name $C_R$ here. \item The axiom $\forall x:\iota,y:\iota.\,R(x,y)\impl C_R(x,y)$, i.e., $C_R$ extends $R$. + \item The axiom $\forall x:\iota.\,C_R(x,x)$, i.e., $C_R$ is reflexive. \item The axiom $\forall x:\iota,y:\iota,z:\iota.\,C_R(x,y)\wedge C_R(y,z)\impl C_R(x,z)$, i.e., $C_R$ is transitive. \end{compactitem} \item We add the case $\sem{R^*}=C_R(x,y)$ to the interpretation function. @@ -625,4 +626,4 @@ \section{Exercise 2} You have to implement that as well or use a library for it. We recommend not focusing on implementing the syntax and semantics in their entirety. -It is more instructive to save time by choosing a sublanguage of BOL (by omitting some productions) and to use the time to implement a second semantics. \ No newline at end of file +It is more instructive to save time by choosing a sublanguage of BOL (by omitting some productions) and to use the time to implement a second semantics. From 169e5ccfadea0112c5d5f34edc9d0e15ed8d0e6c Mon Sep 17 00:00:00 2001 From: ComFreek Date: Thu, 6 Aug 2020 13:26:13 +0200 Subject: [PATCH 04/28] make BOL -> SQL translation more idiomatic --- WuV/bolsem.tex | 33 +++++++++++++++------------------ 1 file changed, 15 insertions(+), 18 deletions(-) diff --git a/WuV/bolsem.tex b/WuV/bolsem.tex index 5024c63..b8c4e06 100644 --- a/WuV/bolsem.tex +++ b/WuV/bolsem.tex @@ -200,8 +200,8 @@ \subsection{Semantics} $F$ & consistency check, consequence closure (omitted)\\ \hline Formula & Query that returns empty result iff formula is true \\ -$C_1 \Equiv C_2$ & $(\sem{C_1}\sm\sem{C_2})$ UNION $(\sem{C_2}\sm\sem{C_1})$\\ -$C_1 \sqsubseteq C_2$ & $\sem{C_1}\sm\sem{C_2}$\\ +$C_1 \Equiv C_2$ & $(\sem{C_1}\text{ EXCEPT }\sem{C_2})$ UNION $(\sem{C_2}\text{ EXCEPT }\sem{C_1})$\\ +$C_1 \sqsubseteq C_2$ & $\sem{C_1}$ EXCEPT $\sem{C_2}$\\ $I\; \texttt{is-a}\; C$ & $\sem{I}$ IN $C$\\ $I_1\; R\; I_2$ & ($\sem{I_1}$, $\sem{I_2}$) IN $R$ \\ $I\; P\; V$ & ($\sem{I}$, $V$) IN $P$ \\ @@ -213,8 +213,8 @@ \subsection{Semantics} $i$ & SELECT * FROM $i$\\ $C_1 \sqcup C_2$ & $\sem{C_1}$ UNION $\sem{C_2}$\\ $C_1 \sqcap C_2$ & $\sem{C_1}$ INTERSECT $\sem{C_2}$\\ -$\forall R.C$ & individuals $\sm$ (SELECT subject FROM $\sem{R}$ WHERE object NOT IN $\sem{C})$ \\ -$\exists R.C$ & SELECT DISTINCT subject FROM $\sem{R}$, $\sem{C}$ WHERE object=id\\ +$\forall R.C$ & individuals EXCEPT (SELECT subject FROM $\sem{R}$ WHERE object NOT IN $\sem{C}$) \\ +$\exists R.C$ & SELECT DISTINCT subject FROM $\sem{R}$ WHERE object IN $\sem{C}$\\ $\dom\, R$ & SELECT DISTINCT subject FROM $\sem{R}$\\ $\rng\, R$ & SELECT DISTINCT object FROM $\sem{R}$\\ $\dom\, P$ & SELECT DISTINCT subject FROM $\sem{P}$\\ @@ -223,8 +223,8 @@ \subsection{Semantics} $i$ & SELECT * FROM $i$\\ $R_1 \cup R_2$ & $\sem{R_1}$ UNION $\sem{R_2}$\\ $R_1 \cap R_2$ & $\sem{R_1}$ INTERSECT $\sem{R_2}$\\ -$R_1 ; R_2$ & SELECT DISTINCT l.subject, r.object FROM $\sem{R_1}$ AS l, $\sem{R_2}$ AS r \\ - & \tb\tb WHERE l.object = r.subject\\ +$R_1 ; R_2$ & SELECT DISTINCT l.subject, r.object FROM $\sem{R_1}$ AS l\\ + & \tb\tb JOIN $\sem{R_2}$ AS r ON l.object = r.subject\\ $R^{-1}$ & SELECT object AS subject, subject AS object FROM $\sem{R}$\\ $R^*$ & (tricky, omitted)\\ $\Delta_C$ & SELECT id AS subject, id AS object FROM $\sem{C}$\\ @@ -232,9 +232,6 @@ \subsection{Semantics} Property of type $T$ & SQL query for two-column table\\ $i$ & SELECT * FROM $i$\\ \end{tabular} -\medskip - -Using the abbreviation: $S\sm T$ = SELECT id FROM $S$ WHERE id NOT IN $T$\\ \caption{Interpretation Function for BOL into SQL}\label{fig:bolsem:sql} \end{figure} @@ -280,16 +277,16 @@ \subsection{Semantics} Moreover, the axioms result in the following consistency checks, i.e., queries that should be empty: \begin{lstlisting} -SELECT * FROM male $\sm$ SELECT * FROM person -SELECT * FROM instructor $\sm$ SELECT * FROM person -SELECT * FROM (SELECT DISTINCT subject FROM teach) $\sm$ SELECT * FROM instructor -SELECT * FROM (SELECT DISTINCT object FROM teach) $\sm$ SELECT * FROM course -(SELECT * FROM (SELECT DISTINCT subject FROM creditValue) $\sm$ SELECT * FROM course) - UNION (SELECT * FROM course $\sm$ SELECT DISTINCT subject FROM creditValue) -SELECT * FROM course $\sm$ +(SELECT * FROM male) EXCEPT (SELECT * FROM person) +(SELECT * FROM instructor) EXCEPT (SELECT * FROM person) +SELECT * FROM (SELECT DISTINCT subject FROM teach) EXCEPT (SELECT * FROM instructor) +SELECT * FROM (SELECT DISTINCT object FROM teach) EXCEPT (SELECT * FROM course) +((SELECT DISTINCT subject FROM creditValue) EXCEPT (SELECT * FROM course)) + UNION ((SELECT * FROM course) EXCEPT (SELECT DISTINCT subject FROM creditValue)) +(SELECT * FROM course) EXCEPT (SELECT DISTINCT subject - FROM (SELECT object AS subject, subject AS object FROM teach), instructor - WHERE object=id) + FROM (SELECT object AS subject, subject AS object FROM teach) + WHERE object IN (SELECT * FROM instructor)) \end{lstlisting} Some of these checks will only succeed after performing the consequence closure. In particular, the table \verb|person| misses the entry $1$ for the individual $\FR$ because the assertion {\FR\;\texttt{is-a}\;\person} is only present as a consequence From 1277f6dc04856d144441440530999df9dcd6bd98 Mon Sep 17 00:00:00 2001 From: ComFreek Date: Thu, 6 Aug 2020 13:40:02 +0200 Subject: [PATCH 05/28] add attribution to copied text --- WuV/onto_general.tex | 1 + 1 file changed, 1 insertion(+) diff --git a/WuV/onto_general.tex b/WuV/onto_general.tex index 872531b..c9fbb10 100644 --- a/WuV/onto_general.tex +++ b/WuV/onto_general.tex @@ -71,6 +71,7 @@ \section{General Principles}\label{sec:onto:principles} This part is commonly called the \textbf{ABox} (A for assertional). \end{compactitem} +Some sentences in following paragraph partially copied from \url{https://en.wikipedia.org/w/index.php?title=Abox&oldid=892872890}. License: \url{https://en.wikipedia.org/w/index.php?title=Special:CiteThisPage&page=Abox&id=892872890&wpFormIdentifier=titleform}. TBox declarations tend to be more permanent within a knowledge base and are used as a schema. In contrast, ABox declarations are much more dynamic in nature and tend to represent instance data. For instance, we can understand relational databases as ontologies made up of table definitions as TBox declarations and table rows as ABox declarations. From 3eae452dbc3e8772b143916ca48ce01756fe75cf Mon Sep 17 00:00:00 2001 From: ComFreek Date: Thu, 6 Aug 2020 13:49:07 +0200 Subject: [PATCH 06/28] make BOL -> Scala translation more idiomatic --- WuV/bolsem.tex | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/WuV/bolsem.tex b/WuV/bolsem.tex index d2f2d18..c8d1982 100644 --- a/WuV/bolsem.tex +++ b/WuV/bolsem.tex @@ -334,7 +334,7 @@ \subsection{Semantics} \kw{individual}\,$i$ & val $i$ = "$i$"; individuals += $i$ \\ \kw{concept}\,$i$ & val $i$ = new HashSet[String]\\ \kw{relation}\,$i$ & val $i$ = new HashSet[(String,String)] \\ -\kw{property}\,$i:T$ & val $i$ = new HashSet[(String,T)] \\ +\kw{property}\,$i:T$ & val $i$ = new HashSet[(String,\sem{T})] \\ $I\; \texttt{is-a}\; C$ & $\sem{C}$ += $\sem{I}$\\ $I_1\; R\; I_2$ & $\sem{R}$ += $(\sem{I_1},\sem{I_2})$\\ $I\; P\; V$ & $\sem{P}$ += $(\sem{I},\sem{V})$\\ @@ -359,9 +359,9 @@ \subsection{Semantics} & \tb r.foreach(x $\rA$ if (!c.contains(x.\_2)) e -= x.\_1); e\} \\ $\exists R.C$ & \{val c = $\sem{C}$; val r = $\sem{R}$; val e = new HashSet[String]; \\ & \tb r.foreach(x$ \rA$ if (c.contains(x.\_2)) e += x.\_1); e\}\\ -$\dom\, R$ & \{val c = new HashSet[String]; $\sem{R}$.foreach(x $\rA$ c += x.\_1); c\}\\ -$\rng\, R$ & \{val c = new HashSet[String]; $\sem{R}$.foreach(x $\rA$ c += x.\_2); c\}\\ -$\dom\, P$ & \{val c = new HashSet[String]; $\sem{P}$.foreach(x $\rA$ c += x.\_1); c\}\\ +$\dom\, R$ & $\sem{R}$.map(\_.\_1).toSet\\ +$\rng\, R$ & $\sem{R}$.map(\_.\_2).toSet\\ +$\dom\, P$ & $\sem{P}$.map(\_.\_1).toSet\\ \hline Relation & HashSet[(String,String)] object\\ $i$ & $i$\\ @@ -369,9 +369,9 @@ \subsection{Semantics} $R_1 \cap R_2$ & $\sem{R_1}$.inter($\sem{R_2}$)\\ $R_1 ; R_2$ & \{val r1 = $\sem{R_1}$; val r2 = $\sem{R_2}$; val e = new HashSet[(String,String)]; \\ & \tb r1.foreach(x $\rA$ r2.foreach(y $\rA$ if (x.\_2 == y.\_1) e += (x.\_1,y.\_2))); e\}\\ -$R^{-1}$ & \{val r = new HashSet[(String,String)]; $\sem{R}$.foreach(x $\rA$ r += (x.\_2,x.\_1)); r\}\\ -$R^*$ & (omitted)\\ -$\Delta_C$ & \{val r = new HashSet[(String,String)]; $\sem{C}$.foreach(x $\rA$ r += (x,x)); r\}\\ +$R^{-1}$ & $\sem{R}$.map(x $\rA$ (x.\_2, x.\_1)).toSet\\ +$R^*$ & (omitted)\\ +$\Delta_C$ & $\sem{C}$.map(x $\rA$ (x, x)).toSet\\ \hline Property of type $T$ & HashSet[(String,T)] object\\ $i$ & $i$\\ From 1306a728033bd70ca8816e7ea82aa3e3a603b436 Mon Sep 17 00:00:00 2001 From: ComFreek Date: Thu, 6 Aug 2020 13:56:07 +0200 Subject: [PATCH 07/28] make BOL -> Scala translation more idiomatic --- WuV/WuV_notes.pdf | Bin 553247 -> 556125 bytes WuV/bolsem.tex | 11 +++++------ 2 files changed, 5 insertions(+), 6 deletions(-) diff --git a/WuV/WuV_notes.pdf b/WuV/WuV_notes.pdf index 767ef5be9fdfdc833c1dfea73d1a575f56291896..c41bc2bfb8d5101401e7d84b135f4ad756d92108 100644 GIT binary patch delta 292913 zcmZUab8sM0oAqPc_DpQswr$%+$2KQ+CicX(F~KAg+qS>it#`L->#OSO>bm{(AGiA6 zuJfGp>-=5Pjc3yO3<9v5;gn1QIsjJg=UgJ>7bvC5igvvM?H|-e7f<#g1FUQq1f*Z 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z&^iC*MU-#XYk)bg@7QvjY9+9uK8yS{^|K9`U;b?Lgv348Ssu1QLE7GCfjO6wDXwrN zP@X2VU-loOf37MxkN$u;7mL}i*n2I6?Gg_NwE z%%Xpe|C|d_9RCqUSc6fZ?H8D0r*;R-*@$?e;aq42Ci%8S1i#gAbH%I(p46BhscbY% zevxnGXDJ_0QnU{iMYs0C0Os7@1(u%!Hn^aO%Q^P>0Whc13XH=%t9$^^{N1TWK7l#q zorwL{E>r=-D9XA3#{C2bM!~2bmTw<)bP^t}`jG4PcQlFw=FAK*r;rKE{D5ak5USF) zgXLxe4%^|Hpu>gnPTFS1eSIkv##&@vb4$STt)g+7h+WN5p16;CM=GP1hn0g*Cq$qg z-mn7~n&G*FE~o~z%sk4$_zUvCcvCWs$vO!4Qnxh$wJ^;l zZ?6chWZ4xz`nf9%|5iJD=r12|;EijrCBX(ARl5-yVc1p=_}+bT*!}k9dc0j z3HvTMFq@wod~kN){K~@Upalz(g_Q+Ca?t$bpdeW||G;$r?*D(66TA6qtgF{7UA4yi TVwc=rNPRVQ=FEc^Egbs4p?Q^h diff --git a/WuV/bolsem.tex b/WuV/bolsem.tex index c8d1982..8cb5078 100644 --- a/WuV/bolsem.tex +++ b/WuV/bolsem.tex @@ -334,16 +334,15 @@ \subsection{Semantics} \kw{individual}\,$i$ & val $i$ = "$i$"; individuals += $i$ \\ \kw{concept}\,$i$ & val $i$ = new HashSet[String]\\ \kw{relation}\,$i$ & val $i$ = new HashSet[(String,String)] \\ -\kw{property}\,$i:T$ & val $i$ = new HashSet[(String,\sem{T})] \\ +\kw{property}\,$i:T$ & val $i$ = new HashSet[(String,$\sem{T}$)] \\ $I\; \texttt{is-a}\; C$ & $\sem{C}$ += $\sem{I}$\\ $I_1\; R\; I_2$ & $\sem{R}$ += $(\sem{I_1},\sem{I_2})$\\ $I\; P\; V$ & $\sem{P}$ += $(\sem{I},\sem{V})$\\ $F$ & assertions, consequence closure (omitted)\\ \hline Formula & Program that evaluates the formula to a Boolean \\ -$C_1 \Equiv C_2$ & \{val $c1$ = $\sem{C_1}$; val $c2$ = $\sem{C_2}$; \\ - & \tb $c_1$.forall(x $\rA$ $c_2$.contains(x)) \&\& $c_2$.forall(x $\rA$ $c_1$.contains(x))\}\\ -$C_1 \sqsubseteq C_2$ & \{val $c1$ = $\sem{C_1}$; val $c2$ = $\sem{C_2}$; $c_1$.forall(x $\rA$ $c_2$.contains(x))\}\\ +$C_1 \Equiv C_2$ & $\sem{C_1}$ == $\sem{C_2}$\\ +$C_1 \sqsubseteq C_2$ & $\sem{C_1}$.subsetOf($\sem{C_2}$)\\ $I\; \texttt{is-a}\; C$ & $\sem{C}$.contains($\sem{I}$)\\ $I_1\; R\; I_2$ & $\sem{R}$.contains($(\sem{I_1},\sem{I_2})$)\\ $I\; P\; V$ & $\sem{P}$.contains($(\sem{I},\sem{V})$)\\ @@ -351,7 +350,7 @@ \subsection{Semantics} Individual & String object\\ $i$ & $i$ \\ \hline -Concept & HashSet[String] object\\ +Concept & Set[String] object\\ $i$ & $i$\\ $C_1 \sqcup C_2$ & $\sem{C_1}$.union($\sem{C_2}$)\\ $C_1 \sqcap C_2$ & $\sem{C_1}$.inter($\sem{C_2}$)\\ @@ -363,7 +362,7 @@ \subsection{Semantics} $\rng\, R$ & $\sem{R}$.map(\_.\_2).toSet\\ $\dom\, P$ & $\sem{P}$.map(\_.\_1).toSet\\ \hline -Relation & HashSet[(String,String)] object\\ +Relation & Set[(String,String)] object\\ $i$ & $i$\\ $R_1 \cup R_2$ & $\sem{R_1}$.union($\sem{R_2}$)\\ $R_1 \cap R_2$ & $\sem{R_1}$.inter($\sem{R_2}$)\\ From 51ef8bece1dc2428c9d392771ce5469bcdadbaea Mon Sep 17 00:00:00 2001 From: ComFreek Date: Thu, 6 Aug 2020 14:44:20 +0200 Subject: [PATCH 08/28] make BOL -> Scala translation more idiomatic --- WuV/bolsem.tex | 28 ++++++++++------------------ 1 file changed, 10 insertions(+), 18 deletions(-) diff --git a/WuV/bolsem.tex b/WuV/bolsem.tex index 8cb5078..bee13e6 100644 --- a/WuV/bolsem.tex +++ b/WuV/bolsem.tex @@ -421,26 +421,18 @@ \subsection{Semantics} Note that we could easily compute the hash set \verb|instructor.diff(male)| and add to it. But that would not add anything to the two constituent sets. -If we thing of the axioms as consistency checks, we can translate them to assertions, i.e., Boolean expressions that must be true. +If we think of the axioms as consistency checks, we can translate them to assertions, i.e., Boolean expressions that must be true. We only give some examples: \begin{lstlisting} -{val c1 = male; val c2 = person; c1.forall(x $\rA$ c2.contains(x))} - -{ - val c1 = course; - val c2 = { - val c = instructor; - val r = { - val r = new HashSet[(String,String)]; - teach.foreach(x $\rA$ r += (x._2,x._1)); - r - } - val e = new HashSet[String]; - r.foreach(x $\rA$ if (c.contains(x._2)) e += x._1); - e - }; - c1.forall(x $\rA$ c2.contains(x)) -} +male.subsetOf(person) + +course.subsetOf({ + val c = instructor; + val r = teach.map(x $\rA$ (x._2, x._1)).toSet; + val e = new HashSet[String]; + r.foreach(x $\rA$ if (c.contains(x._2)) e += x._1); + e +}); \end{lstlisting} %instructor $\sqsubseteq$ person From 08ee11a459cb31ffc61f960f7c0ab0f6e9b7b5e5 Mon Sep 17 00:00:00 2001 From: ComFreek Date: Thu, 6 Aug 2020 14:51:58 +0200 Subject: [PATCH 09/28] typos --- WuV/WuV_notes.pdf | Bin 556125 -> 554977 bytes WuV/bolsem.tex | 2 +- 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/WuV/WuV_notes.pdf b/WuV/WuV_notes.pdf index 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--- a/WuV/bolsem.tex +++ b/WuV/bolsem.tex @@ -589,7 +589,7 @@ \section{Narrative Semantics}\label{sec:bolsem:narr} \item We need a lexicon to obtain inflection information and the translation tries to remedy that by appending ``s'' in various places. This works in some cases but not in others. %\item We have introduced some pattern matching and conditional rules in \Cref{fig:bolsem:eng} to alleviate the greatest awkwardnesses, but much more would be needed, which would lead to things like ``Peter hass Mary'' or ``Peter has as childs Mary''. -\item there are many linguistic devices that serve an important role in natural language, but which we are not targeting. +\item There are many linguistic devices that serve an important role in natural language, but which we are not targeting. An example is plural objects for aggregation. Say we have $P \mathtt{is-a} C$, $M \mathtt{is-a} C$, this would translate to ``P is a $\sem{C}$, M is a $\sem{C}$'' in BOL-pidgin, whereas in natural English we would aggregate this to ``P and M are $\sem{C}$s''. \end{itemize} From 8f7b086021cf284ba6ad98005d78a20fbdf3eddc Mon Sep 17 00:00:00 2001 From: ComFreek Date: Thu, 6 Aug 2020 14:53:53 +0200 Subject: [PATCH 10/28] typos --- WuV/bolsem.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/WuV/bolsem.tex b/WuV/bolsem.tex index 48561cc..1550fcc 100644 --- a/WuV/bolsem.tex +++ b/WuV/bolsem.tex @@ -236,7 +236,7 @@ \subsection{Semantics} \end{figure} \begin{remark}[Limitations] -Our interpretation of BOL in SQL is restricted to assertions using only atomic expressions. +Our interpretation of BOL to SQL is restricted to assertions that use atomic expressions only. For example, in the case for $I$ \texttt{is-a} $C$, we assume that $I$ and $C$ are names. Thus, we have already created an individual for $I$ and a table for $C$, and we can thus insert the former into the latter. The general case would be more complicated but is much less important in practice. 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zy{Mv*)HoS2+x+`K;E8jKuI#ID_OH4^!J9r=B&gkC5acgG85-UM@XTnoU{qL5RBh-4 z+|tJ~xW@0T0)`!ao}g~?d*ucz>iL<*#<4hq1{UW$J#3R{T!n&FJ?4N%#2W*lGs-0q z&*Z-?0zG_g&(p((d==AG6$)M#1ix+wn3IJaKcO=|P2gdujRa=!8d-#40^EH&Am(5% z+6@E@Z;b_*$uD1lXWv)^?%lE%YK06e_CO$?A-4_zrT1_J!UKnyh#3 n+_`PW|Bo^#1OH3(#L}V(rBfyp503&9SnHFhrcDd)>m2oe!5pM9 diff --git a/WuV/bolsem.tex b/WuV/bolsem.tex index 1550fcc..c586988 100644 --- a/WuV/bolsem.tex +++ b/WuV/bolsem.tex @@ -312,6 +312,7 @@ \subsection{Semantics} \item classes for all BOL-base types and values for them (if not already present in Scala) \item classes for individuals and hash sets of objects: \begin{lstlisting} +import scala.collection.immutable.Set import scala.collection.mutable.HashSet val individuals = new HashSet[String] \end{lstlisting} @@ -384,7 +385,8 @@ \subsection{Semantics} $(A,B)$ is the product type $A\times B$ with pairing operator $(x,y)$ and projection functions $\_1$ and $\_2$. $x\rA F(x)$ is $\lambda x.F(x)$. -The class HashSet is part of the standard library and offers function += and -= to add/remove elements, contains to test elementhood, and forall, foreach to quantifiy/iterate over elements. +The class \texttt{Set} is part of the standard library and offers the binary functions inter, union for intersections and unions, subsetOf for subset tests, and functions forall, foreach and map to quantify/iterate over elements. +The class \texttt{HashSet} (from the \texttt{scala.collection.mutable} namespace) provides the same functionality and additionally functions += and -= for adding/removing elements. Types of variables are inferred if omitted. \end{remark} From e4c397aeef461eb3bafa3f67cec26ef06f202e5b Mon Sep 17 00:00:00 2001 From: ComFreek Date: Thu, 6 Aug 2020 15:34:00 +0200 Subject: [PATCH 12/28] detail explanation of why RDF(S)' treatment of individuals and classes is a bit weird from a FOL semantics standpoint --- WuV/WuV_notes.pdf | Bin 555533 -> 555965 bytes WuV/onto_general.tex | 7 ++++--- 2 files changed, 4 insertions(+), 3 deletions(-) diff --git a/WuV/WuV_notes.pdf b/WuV/WuV_notes.pdf index 46af223bf6bdae1b901824ed48ed7a2b5ddcc7b4..7080703a6d3df8cc94fe7a5f57611dcf46f5dc8b 100644 GIT binary patch delta 27284 zcmaic2V9Te_jvENmQos`r8L$1dC%ufLqjREjE0dkWfduecY_o{Qcn>{lrjqyiIPwm zB}pZfEi+Nb_@Bqe_`0{>>+i)&&b{~CbI(2d+(+UE-LgL2ldN%+-5OEjQ?tk2We8hB z9V1m$(#Bl(Kd?{HOm~J^UcTYdPiE5$#*?WD8>NdgL-oAlFL%E`f2zDZR%WYZ??TV{ zbF5tiPpf^e{W#WsVtd%MiyxL0O(8Dka_S1Z$ftcl;pc<$Wq9^iZ&3AmeWFivC5rZdN*U zSI!)2sZiKqZZzb8%F>58gS|yf#U~Q{5?8N+hE4 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Triples}\label{sec:onto:triple} \paragraph{Problems} Reflection is subtle and can easily lead to inconsistencies. -We can see this in how the approach of RDF(S) special entities breaks the semantics via FOL. +We can see this in how the approach of RDF(S) special entities breaks the implicitly intended FOL semantics. -For example, it treats classes both as concepts (when they occur as the object of a concept assertion) and as individuals (when they occur as subject or object of a "rdfs:subClassOf" relation assertion). +For example, it treats classes, e.g. ``instructor'', both as concepts and as individuals. The treatment as a concept happens when a class occurs as the object of a concept assertion, e.g. \texttt{FlorianRabe rdf:type instructor}. By contrast, in relation assertions, e.g. \texttt{instructor rdfs:subclassOf person}, classes appearing as subject or object of such an assertion are treated as individuals. Similarly, "rdfs:Class" is used both as an individual and as a class. In fact, the standard prescribes that "rdfs:Class" is an instance of itself. -In practice, this is handled pragmatically by using ontologies that make sense. +In theory, such ambivalent treatment of one and the same thing as an individual and a class is problematic in FOL. This is because FOL's individual and predicate symbols can neither be inter- nor intramixed in arbitrary ways, e.g., predicates cannot be applied to other predicates. +In practice however, this is handled pragmatically by using ontologies that make sense. A formal way to disentangle this is to assume that there are two variants of "rdfs:Class", one as an individual and one as a class. The translation must then translate "rdfs:Class" differently depending on how it is used. 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QZ8F8S{rYV`VTZQ=AN`-VRR910 diff --git a/WuV/typing.tex b/WuV/typing.tex index 276cdc0..9b315bc 100644 --- a/WuV/typing.tex +++ b/WuV/typing.tex @@ -174,7 +174,7 @@ \subsection{Motivation} \end{lstlisting} It is often desirable to use types to force the presence of such assertions. -We might wish require that every instructor teaches a list of things, and has an office. +We might require that every instructor teaches a list of things and has an office. Moreover, we can use types to specify the objects of the respective assertions: we can specify that only courses are taught and that the office is a string. Rather than the relations with subjects "FlorianRabe" just happening to be around as well, the type system would now force their existence and the type of the object. Forgetting to give such an assertion or giving it with the wrong object could be detected statically (i.e., without applying the semantics) and flagged as a typing error. @@ -193,10 +193,10 @@ \subsection{Motivation} "age" 40 "office" "11.137" \end{lstlisting} -Now the type "instructor" forces the presence of a list of taught courses (The $^*$ is meant to indicate a list.), an integer for the age, and a string for the office. +Now the type "instructor" forces the presence of a list of taught courses (the $^*$ is meant to indicate a list.), an integer for the age, and a string for the office. We can now see that, in fact, every person should have an age, and not just every instructor. -Because every instructor is meant to be a person, we could try to capture this as well to avoid redundancy. +In fact every instructor is meant to be a person, hence we could try to capture this as well to avoid redundancy. Moreover, every male is meant to be a person, too. That leads to the idea of \textbf{modular types}. @@ -391,7 +391,8 @@ \subsection{Rigorous Definition} In the simplest case, we forbid such forward references. Then ADTs are very well-behaved. -But we have a problem with the case $(\ast)$ in Def.~\ref{def:mixinflat}: if $c:T$ occurs before $c:T=t$, we cannot simply drop the former because intermediate fields may refer to $c$. +But we have a problem with the complex case $(\ast)$ in Def.~\ref{def:mixinflat}: if $c:T$ occurs before $c:T=t$, we cannot simply drop the former because intermediate fields may refer to $c$ -- even before the latter field $c:T=t$ appears. + A straightforward solution would be to declare the ADT to be ill-formed. But unfortunately, this case is very important in practice --- it occurs whenever $c:T$ is declared in an abstract class and $c:T=t$ in a concrete class implementing it. 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crucial feature that the language (and type system) must support. +For example in Java, occurrences of overridden fields or methods (often annotated with \texttt{override}) all give rise to some Java-specific way of merging. +Defining a useful yet intuitive way of merging is non-trivial and we elaborate on an exemplary way of doing so and its limitations later. + +TODO: However, this union dependent: if $B$ is flat, its fields may refer to fields introduced in $A$. 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But unfortunately, this case is very important in practice --- it occurs whenever $c:T$ is declared in an abstract class and $c:T=t$ in a concrete class implementing it. -A more common solution is to allow the fields to be mutually recursive. -Consider a flat ADT with fields $\Gamma, c:T[=t], \Delta$ where $\Gamma$ and $\Delta$ are lists of fields. +A more common solution is to allow the fields to be mutually recursive in their definitions. +For example, in an OO-language you can consider two methods that call each other to be a case of two ``fields'' whose types (the method signatures) are \emph{non-recursive} (only backwards-referencing), but whose definitions are mutually recursive. + +Formally, we can capture this as follows. Consider a flat ADT with fields $\Gamma, c:T[=t], \Delta$ where $\Gamma$ and $\Delta$ are lists of fields. Let $\Gamma'$ and $\Delta'$ arise by dropping all definitions. 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diff --git a/WuV/typing.tex b/WuV/typing.tex
index 25b214a..f86b3ec 100644
--- a/WuV/typing.tex
+++ b/WuV/typing.tex
@@ -338,14 +338,14 @@ \subsection{Rigorous Definition}
 \item a \textbf{flat} type of the form
   \[\{c_1:T_1[=t_i],\ldots,c_n:T_n[=t_i]\}\]
   where the $c_i$ are distinct names, the $T_i$ are types, and the $t_i$ are optional and wherever given must have type $T_i$, or
-\item a \textbf{mixin} type of the form $A_1*A_2$ for ADTs $A_i$.
+\item a \textbf{mixin} type of the form $A*B$ for ADTs $A$ and $B$.
 \end{compactitem}
 
 We say that a type system has \textbf{internal ADT}s if all ADTs are types (and thus may in particular occur as the $T_i$ in a record type).
 \end{definition}
 
 The intuition of a mixin $A*B$ is that we \emph{merge} the fields of $A$ and $B$.
-Whereas copying the fields of two ADTs side-by-side is easy and already possible with flat ADTs via $\{c_1: A_1, c_2: A_2\}$ (assuming we have internal ADTs with types $A_i$), merging is a crucial feature that the language (and type system) must support.
+Whereas copying the fields of two ADTs side-by-side is easy and already possible with flat ADTs via $\{c_1: A, c_2: B\}$ (assuming we have internal ADTs), merging is a crucial feature that the language (and type system) must support.
 For example in Java, occurrences of overridden fields or methods (often annotated with \texttt{override}) all give rise to some Java-specific way of merging.
 Defining a useful yet intuitive way of merging is non-trivial and we elaborate on an exemplary way of doing so and its limitations later.
 
@@ -371,6 +371,22 @@ \subsection{Rigorous Definition}
 }
 \end{lstlisting}
 The details can vary, and special care must be taken in programming languages where initialization may have side effects.
+Methods of OO-languages arise as special case of fields whose types are the method signatures and whose definitions are the method bodies.
+For example, the Scala class given by
+\begin{lstlisting}
+//             vvvvvvvvvv this is Scala's syntax for declaring a constructor
+//                        receiving such an argument and storing it in an
+//                        equinamed field
+class NatAdder(val n: nat) {
+  def addAndReturn(m: nat): nat = {
+    return n + m
+  }
+}
+\end{lstlisting}
+could be represented via \[
+  \text{NatAdder} = \texttt{Base} \ast \{n: \mathbb{N}, \text{addAndReturn}: \mathbb{N} \rightarrow \mathbb{N} = \lambda m:\mathbb{N}.\ n + m\}
+\]
+assuming sufficient background knowledge --- e.g., for natural numbers with $\mathbb{N}$ and $+$, function types $\_ \rightarrow \_$, and lambdas $\lambda \_:\_.\ \_$ --- has been declared in some ADT $\text{Base}$ or stems from the underlying  language and type system used.
 
 Flat ADTs are the standard case, and all mixin ADTs can be simplified into flat ones.
 This can be seen as a semantics in the sense that the language of flat and mixin ADT is translated to the language of flat ADTs.
@@ -382,7 +398,7 @@ \subsection{Rigorous Definition}
  $\flt{A}$ arises by concatenating the fields of all $\flt{A_i}$ where duplicate field names are handled as follows:
   \begin{compactitem}
    \item if the same field (same name, types equal, definitions equal or both absent) occurs more than once, only the first occurrence is kept,
-   \item if the fields $c:T_1[=t_i]$ and $c:T_2[=t_2]$ occur for inequal types $T_i$, $A$ is ill-formed,
+   \item if the fields $c:T_1[=t_1]$ and $c:T_2[=t_2]$ occur for inequal types $T_i$, $A$ is ill-formed,
    \item if the fields $c:T=t_1$ and $c:T=t_2$ occur for inequal objects $t_i$, $A$ is ill-formed,
    \item if the fields $c:T=t$ and $c:T$ occur, only the defined one is kept $(\ast)$.
   \end{compactitem}
@@ -395,13 +411,15 @@ \subsection{Rigorous Definition}
 
 In the simplest case, we forbid such forward references.
 Then ADTs are very well-behaved.
-But we have a problem with the complex case $(\ast)$ in Def.~\ref{def:mixinflat}: if $c:T$ occurs before $c:T=t$, we cannot simply drop the former because intermediate fields may refer to $c$ -- even before the latter field  $c:T=t$ appears.
+But we have a problem with the case $(\ast)$ in Def.~\ref{def:mixinflat}: if $c:T$ occurs before $c:T=t$, we cannot simply drop the former because intermediate fields before $c:T=t$ may refer to $c$.
 
 A straightforward solution would be to declare the ADT to be ill-formed.
-But unfortunately, this case is very important in practice --- it occurs whenever $c:T$ is declared in an abstract class and $c:T=t$ in a concrete class implementing it.
+But unfortunately, this case is very important in practice --- it occurs whenever $c:T$ is declared in an abstract class and is overridden via $c:T=t$ in a concrete class implementing it.
 
-A more common solution is to allow the fields to be mutually recursive in their definitions.
-For example, in an OO-language you can consider two methods that call each other to be a case of two ``fields'' whose types (the method signatures) are \emph{non-recursive} (only backwards-referencing), but whose definitions are mutually recursive.
+A more common solution is to allow fields to be not only backwards-referencing, but also forward-referencing, or in general to be mutually recursive.
+This solves case $(\ast)$ since intermediate fields would --- after the removal of $c:T$ --- forward-reference $c:T = t$.
+Indeed, many OO-languages allow a restricted form of mutual recursion, namely that methods of a class may be mutually recursive, or more precisely that method bodies may forward- or backward-reference other methods.
+In ADT tonus, this translates to fields being allowed to forward-reference other fields in their definition; and \emph{only} there, i.e., types of fields can only backward-reference other fields as usual.
 
 Formally, we can capture this as follows. Consider a flat ADT with fields $\Gamma, c:T[=t], \Delta$ where $\Gamma$ and $\Delta$ are lists of fields.
 Let $\Gamma'$ and $\Delta'$ arise by dropping all definitions.

From 383d715a0dfe3960d4568568b394b7612a22724e Mon Sep 17 00:00:00 2001
From: ComFreek 
Date: Mon, 10 Aug 2020 13:16:42 +0200
Subject: [PATCH 17/28] adjust slide on relational databases to how it's done
 in practice

---
 WuV/WuV_slides_body.tex | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/WuV/WuV_slides_body.tex b/WuV/WuV_slides_body.tex
index 9a6fdfc..4d11410 100644
--- a/WuV/WuV_slides_body.tex
+++ b/WuV/WuV_slides_body.tex
@@ -1225,15 +1225,14 @@ \section{Concrete Knowledge and Typed Ontologies}
 
 \begin{blockitems}{Church-Typed Database}
 \item table, column names given in schema
-\item row identified by distinguished column (= key) \\
-options
+\item row identified by distinguished key\\[0.4em]
+options:
  \begin{itemize}
- \item preexistent characteristic column
+ \item preexistent characteristic column or column set
  \item added upon insertion
   \begin{itemize}
   \item UUID string
   \item incremental integers
-  \item concatenation of characteristic list of columns
   \end{itemize} 
  \end{itemize}
 \item column/row identifiers formed by qualifying with table name

From 645c672393b4d0d8d64eb5de345d5c43e471a298 Mon Sep 17 00:00:00 2001
From: ComFreek 
Date: Mon, 10 Aug 2020 13:17:15 +0200
Subject: [PATCH 18/28] typo

---
 WuV/WuV_slides_body.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/WuV/WuV_slides_body.tex b/WuV/WuV_slides_body.tex
index 4d11410..b3347e5 100644
--- a/WuV/WuV_slides_body.tex
+++ b/WuV/WuV_slides_body.tex
@@ -1218,7 +1218,7 @@ \section{Concrete Knowledge and Typed Ontologies}
 \end{frame}
 
 \begin{frame}\frametitle{Identifiers}
-\begin{blockitems}{Curry-Typed Knowledge graph}
+\begin{blockitems}{Curry-Typed Knowledge Graph}
 \item concept, relation, property names given in TBox
 \item individual names attached to nodes
 \end{blockitems}

From 5772e1b5ead2d47afe6d8cbe73acc75396e68952 Mon Sep 17 00:00:00 2001
From: ComFreek 
Date: Mon, 10 Aug 2020 13:26:42 +0200
Subject: [PATCH 19/28] typo

---
 WuV/WuV_slides_body.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/WuV/WuV_slides_body.tex b/WuV/WuV_slides_body.tex
index b3347e5..77d41fc 100644
--- a/WuV/WuV_slides_body.tex
+++ b/WuV/WuV_slides_body.tex
@@ -1270,7 +1270,7 @@ \section{Concrete Knowledge and Typed Ontologies}
 \item field types must be base types, $a:A$ not allowed
 \item allow $ID$ as additional base type
 \item use field $a:ID$ in table $B$
-\item store value of $b$ in table $A$
+\item store value of $a$ in table $A$
 \end{blockitems}
 
 \begin{blockitems}{Inheritance: $B$ inherits from $A$}

From d74d758fda18c45e2088477f3725cb3218ca99c6 Mon Sep 17 00:00:00 2001
From: ComFreek 
Date: Mon, 10 Aug 2020 17:20:43 +0200
Subject: [PATCH 20/28] use substitutions instead of meta-levle functions in
 der. calculus for BOL

---
 WuV/WuV_slides_body.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/WuV/WuV_slides_body.tex b/WuV/WuV_slides_body.tex
index 77d41fc..625d5b7 100644
--- a/WuV/WuV_slides_body.tex
+++ b/WuV/WuV_slides_body.tex
@@ -3772,7 +3772,7 @@ \section{Absolute Semantics for BOL}
 \[\rul{\vdash c\sqsubseteq d \tb \vdash d\sqsubseteq c}{\vdash c\Equiv d}\]
 
 Equal concepts can be substituted for each other:
-\[\rul{\vdash c\Equiv d\tb x:C\vdash f(x):\prop \tb \vdash f(c)}{f(d)}\]
+\[\rul{\vdash c\Equiv d\tb x:C\vdash f:\prop\tb \vdash f[x := c]}{\vdash f[x := d]}\]
 
 \glec{This completely defines equality.}
 \end{frame}
@@ -3809,7 +3809,7 @@ \section{Absolute Semantics for BOL}
 \begin{itemize}
 \item<2-> Open world: no
 \item<3-> Closed world: yes
- \[\rul{\Gamma[x=i]\vdash f[x=i] \;\text{ for every individual } i}{\Gamma, x:I\vdash f(x)}\]
+ \[\rul{\Gamma,x:I \vdash f:\prop\tb\Gamma[x:=i]\vdash f[x:=i] \;\text{ for every ind. } i}{\Gamma, x:I\vdash f}\]
  \glec{effectively applicable if only finitely many individuals}
 \end{itemize}
 \end{frame}

From b63f68ab018ff1a16966a17277747542aa1d0911 Mon Sep 17 00:00:00 2001
From: ComFreek 
Date: Tue, 11 Aug 2020 15:23:10 +0200
Subject: [PATCH 21/28] typo

---
 WuV/WuV_slides_body.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/WuV/WuV_slides_body.tex b/WuV/WuV_slides_body.tex
index 625d5b7..45b88a3 100644
--- a/WuV/WuV_slides_body.tex
+++ b/WuV/WuV_slides_body.tex
@@ -1605,7 +1605,7 @@ \section{Data Types}
  \end{itemize}
 \end{itemize}
 \lec{dependent types much more complicated, less uniformly used}
-\lec{harder to starndardize}
+\lec{harder to standardize}
 \end{frame}
 
 \begin{frame}\frametitle{Collection Data Types}

From 898479cf87e5e4820425628b517f5eaa6ed0d4a5 Mon Sep 17 00:00:00 2001
From: ComFreek 
Date: Tue, 11 Aug 2020 15:31:51 +0200
Subject: [PATCH 22/28] correct syntaxes of JSON, YAML; prettify, too

---
 WuV/WuV_slides_body.tex | 85 ++++++++++++++++++++---------------------
 1 file changed, 42 insertions(+), 43 deletions(-)

diff --git a/WuV/WuV_slides_body.tex b/WuV/WuV_slides_body.tex
index 45b88a3..8ae83ed 100644
--- a/WuV/WuV_slides_body.tex
+++ b/WuV/WuV_slides_body.tex
@@ -1726,14 +1726,14 @@ \section{Data Representation Languages}
 
 \begin{blockitems}{Candidates}
  \item XML: standard on the web, notoriously verbose
- \item JSON: JavaScript objects, more human-friendly text syntax
-  \lec{older than XML, probably better choice than XML in retrospect}
+ \item JSON: minimal, more human-friendly text syntax
+  \lec{newer than XML, very dominant in JS ecosystem}
  \item YAML: line/indentation-based
 \end{blockitems}
 \end{frame}
 
 \begin{frame}{Breakout Question}
-What is the difference between JSON, YAML, XML?
+What is the difference between XML, JSON, and YAML?
 \end{frame}
 
 \begin{frame}\frametitle{Typical Data Representation Languages}
@@ -1753,49 +1753,48 @@ \section{Data Representation Languages}
 \end{blockitems}
 \end{frame}
 
-\begin{frame}\frametitle{Example: JSON}
+\begin{frame}[fragile]\frametitle{Example: JSON}
 JSON:
-\[\mathll{
- \{\\
- \tb "individual": "Florian Rabe",\\
- \tb "age": 40,\\
- \tb "concepts": ["instructor", "male"],\\
- \tb "teach": [\\
- \tb\tb\{"name":"Wuv",credits:7.5\},\\
- \tb\tb\{"name":"KRMT",credits:5\}\\
- \tb]\\
-\}
-}\]
-
+\begin{lstlisting}[basicstyle=\footnotesize]
+{
+  "individual": "FlorianRabe",
+  "age": 40,
+  "concepts": ["instructor", "male"],
+  "teach": [
+    {"name": "WuV", credits: 7.5},
+    {"name": "KRMT", credits: 5}
+  ]
+}
+\end{lstlisting}
 
 Weirdnesses:
 \begin{itemize}
-\item atomic/list/record = basic/array/object
+\item atomic/list/record called basic/array/object
 \item record field names are arbitrary strings, must be quoted
 \item records use $:$ instead of $=$
 \end{itemize}
 \end{frame}
 
-\begin{frame}\frametitle{Example: YAML}
+\begin{frame}[fragile]\frametitle{Example: YAML}
 inline syntax: same as JSON but without quoted field names
 
 alternative: indentation-sensitive syntax
-\[\mathll{
- individual: "Florian Rabe"\\
- age: 40\\
- concepts:\\
- \tb  -\; "instructor"\\
- \tb  -\; "male"\\
- teach:\\
- \tb -\; name: "WuV"\\
- \tb\phantom{-}\; credits: 7.5\\
- \tb  -\; name: "KRMT"\
- \tb\phantom{-}\; credits: 5\\
-}\]
+\begin{lstlisting}[basicstyle=\footnotesize]
+individual: "Florian Rabe"
+age: 40
+concepts:
+  - instructor
+  - male
+teach:
+  - name: WuV
+    credits: 7.5
+  - name: KRMT
+    credits: 5
+\end{lstlisting}
 
 Weirdnesses:
 \begin{itemize}
-\item atomic/list/record = scalar/collection/structure
+\item atomic/list/record called scalar/collection/structure
 \item records use $:$ instead of $=$
 \end{itemize}
 \end{frame}
@@ -1808,22 +1807,22 @@ \section{Data Representation Languages}
 \end{itemize}
 
 \begin{lstlisting}[basicstyle=\footnotesize]
-
- 
-   instructor
-   male
- 
- 
-   
-   
- 
-
+
+  
+    instructor
+    male
+  
+  
+    
+    
+  
+
 \end{lstlisting}
 
 \begin{itemize}
-\item Good: \lstinline|Person|, \lstinline|Course|, \lstinline|Concept| give type of object
+\item Good: \lstinline||, \lstinline||, \lstinline|| give type of object
  \glec{easier to decode}
-\item Bad: value of record field must be string
+\item Bad: values of record fields must be string
  \glec{concepts cannot be given in attribute}
  \glec{integers, Booleans, whitespace-separated lists coded as strings}
 \end{itemize}

From 5393938e0d82da415317732df27796d72c5826e6 Mon Sep 17 00:00:00 2001
From: ComFreek 
Date: Tue, 11 Aug 2020 16:04:13 +0200
Subject: [PATCH 23/28] codecs: pay attention to (un)escaping of things

for strings, we just leave off quotes => no (un)escaping necessary
for encoding lists comma-separatedly, we need to (un)escape the comma
---
 WuV/WuV_slides_body.tex | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/WuV/WuV_slides_body.tex b/WuV/WuV_slides_body.tex
index 8ae83ed..e63ebb8 100644
--- a/WuV/WuV_slides_body.tex
+++ b/WuV/WuV_slides_body.tex
@@ -1832,7 +1832,7 @@ \section{Data Representation Languages}
 \begin{blockitems}{Problem}
 \item Large objects are often redundant
  \glec{specially when machine-produced}
-\item Same string, URL, mathematical objects occurs in multiple places
+\item Same string, URL, mathematical object occurs in multiple places
 \item Handled in memory via pointers
 \item Size of serialization can explode
 \end{blockitems}
@@ -1864,7 +1864,7 @@ \section{Data Representation Languages}
 \item Problem: only works if 
  \begin{itemize}
   \item for immutable data structures
-  \item if no occurrence-specific metadata \glec{e.g., source reference}
+  \item if no occurrence-specific metadata \glec{e.g., source references}
  \end{itemize}
 \end{blockitems}
 
@@ -1925,7 +1925,7 @@ \section{Codecs}
 Easy cases:
 \begin{itemize}
 \item StandardFloat: as specified in IEEE floating point standard
-\item StandardString: as themselves, quoted
+\item StandardString: as themselves
 \item StandardBool: as $true$ or $false$
 \item StandardInt (64-bit): decimal digit-sequences as usual
 \end{itemize}
@@ -1965,18 +1965,19 @@ \section{Codecs}
 \begin{frame}\frametitle{Codecs for Lists}
 Encode list $x$ of elements of type $T$
 \begin{itemize}
-\item $L$ is strings: e.g., comma-separated list of $T$-encoded elements of $x$
+\item $L$ is strings: e.g., comma-separated list of $T$-encoded elements of $x$\\
+\glec{(un)escape comma in T-encoded elements}
 \item $L$ is JSON:
  \begin{itemize}
  \item ListAsString: like for strings above
- \item ListAsArray: lists JSON array of $T$-encoded elements of $x$
+ \item ListAsArray: JSON array of $T$-encoded elements of $x$
  \end{itemize}
 \end{itemize}
 \end{frame}
 
 
 \begin{frame}\frametitle{Additional Types}
-Examples: semester
+Example: semester
 
 Extend BDL:
 \begin{commgrammar}
@@ -1993,7 +1994,7 @@ \section{Codecs}
 \end{frame}
 
 \begin{frame}\frametitle{Additional Types (2)}
-Examples: timestamps
+Example: timestamps
 
 Extend BDL:
 \begin{commgrammar}

From 8456d4dbd9be8b647b82452e8472c01ff53a2178 Mon Sep 17 00:00:00 2001
From: ComFreek 
Date: Tue, 11 Aug 2020 16:15:32 +0200
Subject: [PATCH 24/28] codecs: add note on different endiannesses of ints,
 charsets/encodings of strings of primitive types across languages

---
 WuV/WuV_slides_body.tex | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

diff --git a/WuV/WuV_slides_body.tex b/WuV/WuV_slides_body.tex
index e63ebb8..1fd32b5 100644
--- a/WuV/WuV_slides_body.tex
+++ b/WuV/WuV_slides_body.tex
@@ -1400,7 +1400,9 @@ \section{Motivation}
 \begin{itemize}
 \item essentially the same in every language
  \lec{including whatever language used for semantics}
-\item semantics by translation trivial
+\item semantics by translation straight-forward
+\glec{watch out for different endiannesses for ints,}
+\glec{charsets and encodings for characters/strings}
 \end{itemize}
 \end{frame}
 
@@ -1554,7 +1556,8 @@ \section{Data Types}
  \item IEEE float, double
  \item Booleans
  \item Unicode characters
- \item strings \glec{could be list of characters but usually bad idea}
+ \item strings\\
+ \glec{could be list of characters but usually bad idea}
 \end{blockitems}
 
 \begin{blockitems}{typical in math}

From e56e0e86dfc008bdc7834631615aff897cf5cae4 Mon Sep 17 00:00:00 2001
From: ComFreek 
Date: Tue, 11 Aug 2020 16:25:16 +0200
Subject: [PATCH 25/28] formatting

---
 WuV/WuV_slides_body.tex | 21 ++++++++-------------
 1 file changed, 8 insertions(+), 13 deletions(-)

diff --git a/WuV/WuV_slides_body.tex b/WuV/WuV_slides_body.tex
index 1fd32b5..60a96f8 100644
--- a/WuV/WuV_slides_body.tex
+++ b/WuV/WuV_slides_body.tex
@@ -2105,19 +2105,14 @@ \section{Data Interchange}
 Ontology based on BDL-ADTs with additional codec information:
 \begin{lstlisting}[basicstyle=\footnotesize]
 schema Instructor
-<<<<<<< Updated upstream
-  name:    string      codec StandardString
-  age:     int         codec StandardInt
-  courses: list Course codec CommaSeparatedList CourseAsName
-=======
-  name:     string   codec StandardString
-  age:      int      codec StandardInt
-  courses:  list Course codec CommaSeparatedList CourseAsName
->>>>>>> Stashed changes
+  name:     string        codec StandardString
+  age:      int           codec StandardInt
+  courses:  list Course   codec CommaSepList CourseAsName
+
 schema Course
-  name:     string   codec StandardString
-  credits:  float    codec StandardFloat
-  semester: Semester codec SemesterAsString
+  name:     string        codec StandardString
+  credits:  float         codec StandardFloat
+  semester: Semester      codec SemesterAsString
 \end{lstlisting}
 \medskip
 
@@ -2132,7 +2127,7 @@ \section{Data Interchange}
 
 \begin{frame}\frametitle{Open Problem: Non-Compositionality}
 \begin{blockitems}{Sometimes optimal translation is non-compositional}
-\item example translate $list$-type in ADT to comma-separated string in DB
+\item example translates $list$-type in ADT to comma-separated string in DB
 \item better break up $list\,B$ fields in type $A$ into separate table with columns for $A$ and $B$
 \end{blockitems}
 

From 99a2e4eb5149ad4421be8e12133ab470c265ee62 Mon Sep 17 00:00:00 2001
From: ComFreek 
Date: Tue, 11 Aug 2020 16:46:42 +0200
Subject: [PATCH 26/28] codecs: replace commutation equation by nice tikzcd
 diagram

---
 WuV/WuV_slides.tex      |  1 +
 WuV/WuV_slides_body.tex | 13 ++++++++-----
 2 files changed, 9 insertions(+), 5 deletions(-)

diff --git a/WuV/WuV_slides.tex b/WuV/WuV_slides.tex
index a1400a0..8b99b2c 100644
--- a/WuV/WuV_slides.tex
+++ b/WuV/WuV_slides.tex
@@ -6,6 +6,7 @@
 \usepackage{amsmath}
 \usepackage{amssymb}
 \usepackage{xkeyval}
+\usepackage{tikz-cd}
 
 \usepackage{../macros/mytikz}
 \usepackage{listings}
diff --git a/WuV/WuV_slides_body.tex b/WuV/WuV_slides_body.tex
index 60a96f8..ba5c792 100644
--- a/WuV/WuV_slides_body.tex
+++ b/WuV/WuV_slides_body.tex
@@ -2149,15 +2149,18 @@ \section{Data Interchange}
 \item But queries using semantic operations cannot always be translated to DB
  \begin{itemize}
   \item operation $IsSummer: Semester \to bool$ in BDL
-  \item query \lstinline|SELECT * FROM course WHERE $IsSummer$(semester)|
+  \item query \lstinline|SELECT * FROM course WHERE $\ IsSummer$(semester)|
   \item how to map $IsSummer$ to SQL?
  \end{itemize}
 \item Ontology operations need commuting operations on codes
 \begin{itemize}
-\item given $f: A\to B$ in BDL, codecs $C,D$ for $A$ and $B$
-\item SQL function $f'$ commutes with $f$ iff \\
-  \[B.decode (f'(C.encode\,a)) = f(a)\]
-  for all $a:A$
+\item given $f: T_1\to T_2$ in BDL between types $T_{1,2}$ and respective codecs $C_{1,2}$ into representation language $L$,
+\item SQL function $f'$ commutes with $f$ iff \[
+  \begin{tikzcd}[ampersand replacement=\&]
+    T_1 \arrow[d, "C_1.encode"'] \arrow[r, "f"] \& T_2\\
+    L \arrow[r, "f'"] \& L \arrow[u, "C_2.decode"']
+  \end{tikzcd}
+\]
 \end{itemize}
 \end{itemize}
 \end{frame}

From aec59cb71715c0f01496bd4fd82ec2ea185fe1f9 Mon Sep 17 00:00:00 2001
From: ComFreek 
Date: Tue, 11 Aug 2020 16:50:38 +0200
Subject: [PATCH 27/28] clean up query commutation slide

---
 WuV/WuV_slides.pdf      | Bin 1896764 -> 1913992 bytes
 WuV/WuV_slides_body.tex |   8 ++++----
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/WuV/WuV_slides.pdf b/WuV/WuV_slides.pdf
index 6db8aba84ab6bf34c64732a4c81ee1478a18e22b..8a9a9349491d48c5e8e4bc96256d08c3b07e7a2d 100644
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respective codecs $C_{1,2}$ into representation language $L$, -\item SQL function $f'$ commutes with $f$ iff \[ +\item given $f: T_1\to T_2$ in BDL and respective codecs $C_{1,2}$, +\item $L$-function $f'$ commutes with $f$ iff \[ \begin{tikzcd}[ampersand replacement=\&] T_1 \arrow[d, "C_1.encode"'] \arrow[r, "f"] \& T_2\\ L \arrow[r, "f'"] \& L \arrow[u, "C_2.decode"'] From bb128e5fc44325e082b6039b0d295d7a919fb21c Mon Sep 17 00:00:00 2001 From: ComFreek Date: Thu, 13 Aug 2020 14:54:41 +0200 Subject: [PATCH 28/28] typo --- WuV/WuV_slides.pdf | Bin 1913992 -> 1913992 bytes WuV/WuV_slides_body.tex | 4 ++-- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/WuV/WuV_slides.pdf b/WuV/WuV_slides.pdf index 8a9a9349491d48c5e8e4bc96256d08c3b07e7a2d..1f3540b836ebe19833300a9a38ba022ad0791d86 100644 GIT binary patch delta 159 zcmeBpS<>;cq@jheg{g(Pg{6hHg{_6Xg`WaPoD?RULoyk0sRyI7c5Sely~x)>X~I+;2- eTbP+xni!ZkI=WdpS(q5wDcBHFGCj*gRt^AJcP!li delta 159 zcmeBpS<>;cq@jheg{g(Pg{6hHg{_6Xg`