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DOI: 10.4230/OASIcs.ICLP.2016.14

A Compositional Typed Higher-Order Logic with Definitions

Authors: Ingmar Dasseville, Matthias van der Hallen, Bart Bogaerts, Gerda Janssens, and Marc Denecker

Published in: OASIcs, Volume 52, Technical Communications of the 32nd International Conference on Logic Programming (ICLP 2016)

Abstract

Expressive KR languages are built by integrating different language constructs, or extending a language with new language constructs. This process is difficult if non-truth-functional or non-monotonic constructs are involved. What is needed is a compositional principle. This paper presents a compositional principle for defining logics by modular composition of logical constructs, and applies it to build a higher order logic integrating typed lambda calculus and rule sets under a well-founded or stable semantics. Logical constructs are formalized as triples of a syntactical rule, a semantical rule, and a typing rule. The paper describes how syntax, typing and semantics of the logic are composed from the set of its language constructs. The base semantical concept is the infon: mappings from structures to values in these structures. Semantical operators of language constructs operate on infons and allow to construct the infons of compound expressions from the infons of its subexpressions. This conforms to Frege's principle of compositionality.

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Ingmar Dasseville, Matthias van der Hallen, Bart Bogaerts, Gerda Janssens, and Marc Denecker. A Compositional Typed Higher-Order Logic with Definitions. In Technical Communications of the 32nd International Conference on Logic Programming (ICLP 2016). Open Access Series in Informatics (OASIcs), Volume 52, pp. 14:1-14:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{dasseville_et_al:OASIcs.ICLP.2016.14,
  author =	{Dasseville, Ingmar and van der Hallen, Matthias and Bogaerts, Bart and Janssens, Gerda and Denecker, Marc},
  title =	{{A Compositional Typed Higher-Order Logic with Definitions}},
  booktitle =	{Technical Communications of the 32nd International Conference on Logic Programming (ICLP 2016)},
  pages =	{14:1--14:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-007-1},
  ISSN =	{2190-6807},
  year =	{2016},
  volume =	{52},
  editor =	{Carro, Manuel and King, Andy and Saeedloei, Neda and De Vos, Marina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ICLP.2016.14},
  URN =		{urn:nbn:de:0030-drops-67447},
  doi =		{10.4230/OASIcs.ICLP.2016.14},
  annote =	{Keywords: Logic, Semantics, Compositionality}
}

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DOI: 10.4230/LIPIcs.ICLP.2010.124

Dedicated Tabling for a Probabilistic Setting

Authors: Theofrastos Mantadelis and Gerda Janssens

Published in: LIPIcs, Volume 7, Technical Communications of the 26th International Conference on Logic Programming (2010)

Abstract

ProbLog is a probabilistic framework that extends Prolog with probabilistic facts. To compute the probability of a query, the complete SLD proof tree of the query is collected as a sum of products. ProbLog applies advanced techniques to make this feasible and to assess the correct probability. Tabling is a well-known technique to avoid repeated subcomputations and to terminate loops. We investigate how tabling can be used in ProbLog. The challenge is that we have to reconcile tabling with the advanced ProbLog techniques. While standard tabling collects only the answers for the calls, we do need the SLD proof tree. Finally we discuss how to deal with loops in our probabilistic framework. By avoiding repeated subcomputations, our tabling approach not only improves the execution time of ProbLog programs, but also decreases accordingly the memory consumption. We obtain promising results for ProbLog programs using exact probability inference.

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Theofrastos Mantadelis and Gerda Janssens. Dedicated Tabling for a Probabilistic Setting. In Technical Communications of the 26th International Conference on Logic Programming. Leibniz International Proceedings in Informatics (LIPIcs), Volume 7, pp. 124-133, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{mantadelis_et_al:LIPIcs.ICLP.2010.124,
  author =	{Mantadelis, Theofrastos and Janssens, Gerda},
  title =	{{Dedicated Tabling for a Probabilistic Setting}},
  booktitle =	{Technical Communications of the 26th International Conference on Logic Programming},
  pages =	{124--133},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-17-0},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{7},
  editor =	{Hermenegildo, Manuel and Schaub, Torsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICLP.2010.124},
  URN =		{urn:nbn:de:0030-drops-25903},
  doi =		{10.4230/LIPIcs.ICLP.2010.124},
  annote =	{Keywords: Tabling, Loop Detection, Probabilistic Logical Programming, ProbLog}
}

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Documents authored by Janssens, Gerda

A Compositional Typed Higher-Order Logic with Definitions

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Dedicated Tabling for a Probabilistic Setting

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