Making dynamic logic first-order
Regular dynamic logic DL is given an alternative semantics admitting non-standard interpretation of arithmetical notions and, consequently, of finiteness; the interpretation of iteration of a program is made dependent on this, possibly non-standard notion of finiteness. Dynamic logic with this semantics is recursively axiomatizable: roughly speaking, Harel's axioms and deduction rules together with axioms of Peano arithmetic form a finitary sound and complete axiomatization of valid formulas.
KeywordsDynamic Logic Peano Arithmetic Deduction Rule Full Induction Complete Axiomatization
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