This paper discusses a new strategy to decide Dummett logic. The strategy relies on a tableau calculus whose distinguishing features are the rules for implicative formulas. The strategy has been implemented and the experimental results are reported.

In this paper, we introduce the notionofWajsberg implicative ideal(WI-ideal)of lattice Wajsberg algebra.Further, we definelattice H-Wajsberg algebra, implication homomorphismand lattice implication homomorphism oflattice Wajsberg algebra. Finally, we give kernel of implication homomorphism and obtain some oftheir properties.

This paper studies, with techniques of Abstract Algebraic Logic, the effects of putting a bound on the cardinality of the set of side formulas in the Deduction Theorem, viewed as a Gentzen-style rule, and of adding additional assumptions inside the formulas present in Modus Ponens, viewed as a Hilbert-style rule. As a result, a denumerable collection of new Gentzen systems and two new sententia...

In this thesis we study the problems of distance approximation to monotonicity and distance approximation to convexity. Namely, we are interested in (randomized) sublinear algorithms that approximate the Hamming distance between a given function and the closest monotone/convex function. For the monotonicity property, we focus on functions over the d-dimensional hyper-cube, [n]d, with any finite...

We introduce the notion of ideals in implicative semigroups, and then state the characterizations of the ideals. 2000 Mathematics Subject Classification. 20M12, 06F05, 06A06, 06A12.

The main aim of this work is to introduce and study the notions ideal direct product d-algebras, d-ideal sub-direct edge positive implicative d-algebras investigate their characterizations.

Recently W. McCune and D. A. Sands have considered, in a note Amer Math. Monthly 103 (1996), 888{892], implicative axioms in groups of the form if u = v, then w = t, where u, v, w, t are group words in some variables. Their interest is in such identical implications that deene the variety of groups, or the variety of abelian groups. What I want to present is, slightly more generally, identical ...