Algebraic properties of the space of multivalued and paraconsistent logic programs

V. S. Subrahmanian*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Paraconsistent logics are a class of logics proposed by Newton da Costa [7] that provide a framework for formal reasoning about inconsistent systems. In [4, 5, 6], Blair and Subrahmanian, and independently, Fitting [11], showed that paraconsistent logics may be successfully used for logic programming. In this paper, we study the algebraic properties of the space of paraconsistent logic programs over a complete lattice of truth values. We show that this set, under some natural operations generalizing those defined by Mancarella and Pedreschi [18], yields a distributive lattice that satisfies various important non-extensibility conditions. Intuitively, these non-extensibility conditions tell us that the algebraic characterization we provide cannot be (naturally) strengthened any further. As an interesting application, we generalize the notion of subsumption equivalence of classical logic programs to the case of multi-valued logic programs and derive necessary and sufficient conditions for multivalued logic programs to be subsumption-equivalent.

Original languageEnglish (US)
Title of host publicationFoundations of Software Technology and Theoretical Computer Science - 9th Conference, Proceedings
EditorsC.E. Veni Madhavan
PublisherSpringer Verlag
Pages56-67
Number of pages12
ISBN (Print)9783540520481
DOIs
StatePublished - 1989
Externally publishedYes
Event9th Conference on Foundations of software Technology and Theoretical Computer Science, FST and TCS 1989 - Bangalore, India
Duration: Dec 19 1989Dec 21 1989

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume405 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference9th Conference on Foundations of software Technology and Theoretical Computer Science, FST and TCS 1989
Country/TerritoryIndia
CityBangalore
Period12/19/8912/21/89

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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