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General Logic Programs as Infinite Games

Authors: Chrysida Galanaki, Panos Rondogiannis, and William W. Wadge

Published in: Dagstuhl Seminar Proceedings, Volume 8271, Topological and Game-Theoretic Aspects of Infinite Computations (2008)

Abstract

In [vE86] M.H. van Emden introduced a simple game semantics for definite logic programs. Recently [RW05,GRW05], the authors extended this game to apply to logic programs with negation. Moreover, under the assumption that the programs have a finite number of rules, it was demonstrated in [RW05,GRW05] that the game is equivalent to the well-founded semantics of negation. In this paper we present work-in-progress towards demonstrating that the game of [RW05,GRW05] is equivalent to the well-founded semantics even in the case of programs that have a countably infinite number of rules. We argue however that in this case the proof of correctness has to be more involved. More specifically, in order to demonstrate that the game is correct one has to define a refined game in which each of the two players in his first move makes a bet in the form of a countable ordinal. Each ordinal can be considered as a kind of clock that imposes a "time limit" to the moves of the corresponding player. We argue that this refined game can be used to give the proof of correctness for the countably infinite case.

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Chrysida Galanaki, Panos Rondogiannis, and William W. Wadge. General Logic Programs as Infinite Games. In Topological and Game-Theoretic Aspects of Infinite Computations. Dagstuhl Seminar Proceedings, Volume 8271, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{galanaki_et_al:DagSemProc.08271.5,
  author =	{Galanaki, Chrysida and Rondogiannis, Panos and Wadge, William W.},
  title =	{{General Logic Programs as Infinite Games}},
  booktitle =	{Topological and Game-Theoretic Aspects of Infinite Computations},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8271},
  editor =	{Peter Hertling and Victor Selivanov and Wolfgang Thomas and William W. Wadge and Klaus Wagner},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08271.5},
  URN =		{urn:nbn:de:0030-drops-16519},
  doi =		{10.4230/DagSemProc.08271.5},
  annote =	{Keywords: Infinite Games, Negation in Logic Programming, Well-Founded Semantics}
}

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DOI: 10.4230/DagSemProc.08271.6

On the Semantic Approaches to Boolean Grammars

Authors: Vassilis Kountouriotis, Christos Nomikos, and Panos Rondogiannis

Published in: Dagstuhl Seminar Proceedings, Volume 8271, Topological and Game-Theoretic Aspects of Infinite Computations (2008)

Abstract

Boolean grammars extend context-free grammars by allowing conjunction and negation in rule bodies. This new formalism appears to be quite expressive and still efficient from a parsing point of view. Therefore, it seems reasonable to hope that boolean grammars can lead to more expressive tools that can facilitate the compilation process of modern programming languages. One important aspect concerning the theory of boolean grammars is their semantics. More specifically, the existence of negation makes it difficult to define a simple derivation-style semantics (such as for example in the case of context-free grammars). There have already been proposed a number of different semantic approaches in the literature. The purpose of this paper is to present the basic ideas behind each method and identify certain interesting problems that can be the object of further study in this area.

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Vassilis Kountouriotis, Christos Nomikos, and Panos Rondogiannis. On the Semantic Approaches to Boolean Grammars. In Topological and Game-Theoretic Aspects of Infinite Computations. Dagstuhl Seminar Proceedings, Volume 8271, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{kountouriotis_et_al:DagSemProc.08271.6,
  author =	{Kountouriotis, Vassilis and Nomikos, Christos and Rondogiannis, Panos},
  title =	{{On the Semantic Approaches to Boolean Grammars}},
  booktitle =	{Topological and Game-Theoretic Aspects of Infinite Computations},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8271},
  editor =	{Peter Hertling and Victor Selivanov and Wolfgang Thomas and William W. Wadge and Klaus Wagner},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08271.6},
  URN =		{urn:nbn:de:0030-drops-16527},
  doi =		{10.4230/DagSemProc.08271.6},
  annote =	{Keywords: Boolean Grammars, Negation in Formal Grammars, Well-Founded Semantics}
}

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General Logic Programs as Infinite Games

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On the Semantic Approaches to Boolean Grammars

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