We show that simultaneous rigid E-uni cation, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable. This result implies that the 8 98 fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the 99-fragment, we obtain a complete classi cation of decidability of the prenex fragment of intuitio...

A minimal theorem in a logic L is an L-theorem which is not a nontrivial substitution instance of another L-theorem. Komori (1987) raised the question whether every minimal impli-cational theorem in intuitionistic logic has a unique normal proof in the natural deduction system NJ. The answer has been known to be partially positive and generally negative. It is shown here that a minimal implicat...

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.

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).

The dynamic multi-attribute decision making problems with intuitionistic fuzzy information are investigated. The notions of intuitionistic fuzzy variable and uncertain intuitionistic fuzzy variable are defined, and two new aggregation operators: dynamic intuitionistic fuzzy weighted averaging (DIFWA) operator and uncertain dynamic intuitionistic fuzzy weighted averaging (UDIFWA) operator are pr...

The purpose of this paper is to introduce and study the concepts of fuzzy $e$-open set, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy $e$-open sets and intuitionistic fuzzy $e$-continuity and other results re...

Bi-intuitionistic logic is a conservative extension of intuitionistic logic with a connective dual to implication, called exclusion. We present a sound and complete cut-free labelled sequent calculus for bi-intuitionistic propositional logic, BiInt, following S. Negri’s general method for devising sequent calculi for normal modal logics. Although it arises as a natural formalization of the Krip...

This paper provides a call-by-name and a call-by-value term calculus, both of which have a Curry-Howard correspondence to the box fragment of the intuitionistic modal logic IK. The strong normalizability and the confluency of the calculi are shown. Moreover, we define a CPS transformation from the call-by-value calculus to the call-by-name calculus, and show its soundness and completeness.

Let T be a first-order theory. A T -normal Kripke structure is one in which every world is a classical model of T . This paper gives a characterization of the intuitionistic theory HT of sentences intuitionistically valid (forced) in all T -normal Kripke structures and proves the corresponding soundness and completeness theorems. For Peano arithmetic (PA), the theory HPA is a proper subtheory o...