Completeness for Ancestral Logic via a Computationally-Meaningful Semantics

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations

Abstract

First-order logic (FOL) is evidently insufficient for the many applications of logic in computer science, mainly due to its inability to provide inductive definitions. Therefore, only an extension of FOL which allows finitary inductive definitions can be used as a framework for automated reasoning. The minimal logic that is suitable for this goal is Ancestral Logic (AL), which is an extension of FOL by a transitive closure operator. In order for AL to be able to serve as a reasonable (and better) substitute to the use of FOL in computer science, it is crucial to develop adequate, user-friendly proof systems for it. While the expressiveness of AL renders any effective proof system for it incomplete with respect to the standard semantics, there are useful approximations. In this paper we show that such a Gentzen-style approximation is both sound and complete with respect to a natural, computationally-meaningful Henkin-style semantics for AL.

Original languageEnglish
Title of host publicationAutomated Reasoning with Analytic Tableaux and Related Methods - 26th International Conference, TABLEAUX 2017, Proceedings
EditorsClaudia Nalon, Renate A. Schmidt
PublisherSpringer Verlag
Pages247-260
Number of pages14
ISBN (Print)9783319669014
DOIs
StatePublished - 1 Jan 2017
Externally publishedYes
Event26th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2017 - Brasilia, Brazil
Duration: 25 Sep 201728 Sep 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10501 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference26th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2017
Country/TerritoryBrazil
CityBrasilia
Period25/09/1728/09/17

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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