1. A Deductive System for PC(ID)
- Author
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Johan Wittocx, Marc Denecker, Ping Hou, Baral, C, Brewka, G, and Schlipf, J
- Subjects
Computer science ,Zeroth-order logic ,Well-formed formula ,Inference ,Intermediate logic ,Intuitionistic logic ,computer.software_genre ,Tautology (logic) ,Formal proof ,Description logic ,Proof calculus ,Sequent ,Rule of inference ,Autoepistemic logic ,Logic programming ,Soundness ,Discrete mathematics ,Propositional variable ,Natural deduction ,Programming language ,Second-order logic ,Classical logic ,Sequent calculus ,Resolution (logic) ,Propositional calculus ,First-order logic ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Disjunction introduction ,TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS ,Many-valued logic ,Dynamic logic (modal logic) ,computer - Abstract
The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. This paper studies a deductive inference method for PC(ID), its propositional fragment. We introduce a formal proof system based on the sequent calculus (Gentzen-style deductive system) for this logic. As PC(ID) is an integration of classical prepositional logic and propositional inductive definitions, our deductive system integrates inference rules for propositional calculus and definitions. We prove the soundness and completeness of this deductive system for a slightly restricted fragment of PC(ID). We also give a counter-example to show that cut-elimination does not hold in this proof system. © Springer-Verlag Berlin Heidelberg 2007. ispartof: pages:162-174 ispartof: Lecture Notes in Computer Science vol:4483 pages:162-174 ispartof: Logic Programming and Nonmonotonic Reasoning location:Tempe, AZ, USA date:15 May - 17 May 2007 status: published
- Published
- 2007
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