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Representing any-time and program-iteration by infinitary conjunction. (English) Zbl 1398.03094
Summary: Two new infinitary modal logics are simply obtained from a Gentzen-type sequent calculus for infinitary logic by adding a next-time operator, and a program operator, respectively. It is shown that an any-time operator and a program-iteration operator can respectively be expressed using infinitary conjunction in these logics. The cut-elimination and completeness theorems for these logics are proved using some theorems for embedding these logics into (classical) infinitary logic.
03B45 Modal logic (including the logic of norms)
03C75 Other infinitary logic
03F05 Cut-elimination and normal-form theorems
Full Text: DOI
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