abstract introduction: scaling and root planing is one of the most commonly used procedures during periodontal treatments. removal of calculus using conventional hand instruments is incomplete and rather time consuming. to find more efficient and less difficult instrumentation method, investigators have proposed lasers as an alternative or adjunct to hand instruments for scaling and root planin...

This paper proposes an expansion of set of primitive constraints available within the Primitive Optimality Theory framework (Eisner, 1997a). This expansion consists of the addition of a new family of constraints—existential implicational constraints, which allow the specification of faithfulness constraints that can be satisfied at a distance—and the definition of two ways to combine simple con...

We prove confluence of two cut-elimination procedures for the implicational fragment of a standard intuitionistic sequent calculus. One of the cut-elimination procedures uses global proof transformations while the other consists of local ones. Both of them include permutation of cuts to simulate β-reduction in an isomorphic image of the λ-calculus. We establish the confluence properties through...

A formula is said to have unique-normal proof property and unique-normal proof property ii it has a unique-normal proof and a-normal proof in NJ, respectively. In this report a condition of implicational minimal formulas in the intuitionistic logic for unique-normal proof property is presented making use of unique-normal proof property for negatively non-duplicated formulas. It is shown that th...

Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which suffices...

This paper describes an algorithm of proof search for implicational formula in intuitionistic logic. It is based on a natural deduction style formulation of long normal form of simply typed -calculus. The algorithm returns a deduction tree, which becomes a proof if the formula is provable. When the formula is unprovable, a counter-model is constructed by identifying the repeated nodes in the de...

We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry–Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without any restriction. Its type system enforces strong normalization of expressions and it is a sound and complete system for full implicational Classical Logic. W...

– from a linguistic perspective – from a formal perspective • Locality of grammatical relations in HPSG 3 HPSG grammars from a linguistic perspective From a linguistic perspective, an HPSG grammar consists of • a lexicon licensing basic words • lexical rules licensing derived words • immediate dominance (id) schemata licensing constituent structure • linear precedence (lp) statements constraini...

In this contribution we present uniform goal-directed rules for the implicational fragments of the three main formalizations of fuzzy logic; namely, Łukasiewicz logic Ł, Gödel logic G, and Product logic Π. We begin with a historical overview of the goal-directed methodology, focussing in particular on the pioneering work of Dov Gabbay, then proceed by recalling the fundamental systems of fuzzy ...