We prove a quadratic upper bound for the depth of cut free proofs in propositional intuitionistic logic formalized with Gentzen’s sequent calculus. We discuss bounds on the necessary number of reuses of left implication rules. We exhibit an example showing that this quadratic bound is optimal. As a corollary, this gives a new proof that propositional validity for intuitionistic logic is in PSPACE.

Usually, in the Kripke semantics for intuitionistic propositional logic (or for superintuitionistic logics) partially ordered frames are used. Why? In this paper we propose an intrinsically intuitionistic motivation for that. Namely, we show that every Kripke frame (with an arbitrary accessibility relation), whose set of valid formulas is a superintuitionistic logic, is logically equivalent to ...

MIPC is a well-known intuitionistic modal logic of Prior (1957) and Bull(1966). It is shown that every normal intuitionistic modal logic L over MIPC has the nite model property whenever L is Kripke-complete and universal. Mathematics Subject Classi cation: 03B45, 03B25.

Since then, our Dangerous Reductions research [HHU07] was accepted at the SAT 2007 conference in Lisbon. In light of Pavel Hrubes’ recent impressive Intuitionistic Logic lower bounds [Hru06], we are currently in the process of reworking our Intuitionistic Logic paper, which needs to be modified to take the new results into account. In unrelated research, [HHM07] was recently accepted by the Not...

In this paper we introduce Fresh Logic, a natural deduction style first-order logic extended with term-formers and quantifiers derived from the FM-sets model of names and binding in abstract syntax. Fresh Logic can be classical or intuitionistic depending on whether we include a law of excluded middle; we present a proof-normalisation procedure for the intuitionistic case and a semantics based ...

We show finite model property, disjunction property and decidability for an intuitionistic epistemic logic IEC. Intuitionistic logic is originally a formalisation of a single mathematician whose knowledge increases over time. The logic IEC formalises multiple agents that communicate asynchronously and whose knowledge increases over time. Although soundness and strong completeness for IEC for a ...

It is shown that every normal intuitionistic modal logic L over MIPC has the nite model property if there exists a universal rstorder sentence such that (1) L is characterized by the class of Kripke frames satisfying and (2) every Kripke frame that validates L satis es . Here, MIPC is a well-known intuitionistic modal logic introduced by Prior (1957).

We reconsider Rauszer’s bi-intuitionistic logic in the framework of the logic for pragmatics: every formula is regarded as expressing an act of assertion or conjecture, where conjunction and implication are assertive and subtraction and disjunction are conjectural. The resulting system of polarized bi-intuitionistic logic (PBL) consists of two fragments, positive intuitionistic logic LJ and its...

We show that the model checking problem for intuitionistic propositional logic with one variable is complete for logspace-uniform AC1. The basic tool we use is the connection between intuitionistic logic and Heyting algebras, investigating its complexity theoretical aspects. For superintuitionistic logics with one variable, we obtain NC1-completeness for the model checking problem.