The decidability of one-variable propositional calculi.

The Decidability of Simultaneous Rigid E-Unification with One Variable

We show that simultaneous rigid E-unification, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable. This result implies that the ∀∗∃∀∗ fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the ∃∃-fragment, we obtain a complete classification of decidability of the prenex fragment of intui...

Decidability and Undecidability Results for Propositional Schemata

We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions (e.g., pi) and iterated connectives ∨ or ∧ ranging over intervals parameterized by arithmetic variables (e.g., ∧n i=1 pi, where n is a parameter). The satisfiability problem is shown to be undecidable for this new logic, but we introduce a very general class of schemata, called b...

Classical Propositional Decidability via Nuprl Proof Extraction

This paper highlights a methodology of Nuprl proof that re sults in e cient programs that are more readable than those produced by other established methods for extracting programs from proofs We de scribe a formal constructive proof of the decidability of a sequent calculus for classical propositional logic The proof is implemented in the Nuprl system and the resulting proof object yields a co...

On non-local propositional and one-variable quantified CTL

Sebastian Bauer,1 Ian Hodkinson,2 Frank Wolter,3 and Michael Zakharyaschev4 1;3Institut für Informatik, Universität Leipzig, Augustus-Platz 10-11, 04109 Leipzig, Germany; 2Department of Computing, Imperial College, 180 Queen’s Gate, London SW7 2BZ, U.K.; 4Department of Computer Science, King’s College, Strand, London WC2R 2LS, U.K. (e-mails: fbauer,[email protected], [email protected]....

The Decidability of Dependency in Intuitionistic Propositional Logic