It is show11 that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives. including those proposed by Gabbay. are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases. the double negatio~l of such a connective is equivalent to a formula of intnitionistic calculus. Thus, under the excluded third law i...

We develop a denotational, fully abstract semantics for constraint logic programming (clp) with respect to successful and failed observables. The denotational approach turns out very useful for the deenition of new operators on the language as the counterpart of some abstract operations on the denotational domain. In particular, by deening our domain as a cylindric Heyting algebra, we can explo...

Abstract A deductive system is said to be structurally complete if its admissible rules are derivable. In addition, it called hereditarily all extensions complete. Citkin (1978) proved that an intermediate logic and only the variety of Heyting algebras associated with omits five finite algebras. Despite importance in theory rules, a direct proof Citkin’s theorem not widely accessible. this pape...

Axiomatizability, the finite model property (FMP), and decidability are some of the most frequently studied properties of non-classical logics. One of the first general methods of axiomatizing large classes of superintuitionistic logics (si-logics for short) was developed by Jankov [8]. For each finite subdirectly irreducible Heyting algebra A, Jankov designed a formula that encodes the structu...

Let A be a 4nitely generated variety of Heyting algebras and let SI(A) be the class of subdirectly irreducible algebras in A. We prove that A is dually equivalent to a category of functors from SI(A) into the category of Boolean spaces. The main tool is the theory of multisorted natural dualities. c © 2002 Elsevier Science B.V. All rights reserved. MSC: Primary: 06D20; 06D50; secondary: 08C05; ...

In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that $ell^1(S)$ is  a symmetric $ell^1(E)$-module amenable if and only if $S$ is amenable, where $S$ is an inverse semigroup with subsemigr...

We study Nonassociative Lambek Calculus with additives ∧,∨, satisfying the distributive law (Full Nonassociative Lambek Calculus with Distribution DFNL). We prove that formal grammars based on DFNL, also with assumptions, generate context-free languages. The proof uses proof-theoretic tools (interpolation) and a construction of a finite model, employed in [13] in the proof of Strong Finite Mode...