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Extension of PDL and consequence relations

  • Slavian Radev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 208)

Abstract

Most of the deduction algorithms are of the form of regular expressions. To investigate some properties of these deductions we introduce an extension of PDL with propositional constants and infinite conjunctions and disjunctions. We treat the formulas of the object logical language for which the deductions are as propositional variables, the sets of formulas — as propositional constants and the deductions — as regular programs. A Hilbert's style axiomatization of this logic is shown to be complete for countable Kripke structures of sets of formulas.

Examples include a logic for the PDL logical consequences, a kind of a nonmonotonic deduction algorithm and some properties of logical consequences.

Keywords

PDL infinitary logic logical consequence relations deduction methods artificial intelligence monotonicity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Slavian Radev
    • 1
  1. 1.Section of Mathematical LogicInstitute of Mathematics, BANSofiaBulgaria

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