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.
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