Beck [1] developed cognitive therapy which led to broad therapeutic innovations and successful applications in the field of psychotherapy [2-4]. Mostly, by virtue of its linear nature and lack of empirical support from cognitive science, this clinically-driven model faced some limitations in practice [5]. To overcome the shortcomings, Teasdale and Barnard [6] experimentally investigated the lin...

Based on the fully implicational idea, we investigate the interval-valued fuzzy reasoning with multiantecedent rules. First, we construct a class of interval-valued fuzzy implications by means of a type of implications and a parameter on the unit interval, then use them to establish three kinds of fully implicational reasoning methods for the interval-valued fuzzy reasoning with multi-anteceden...

In 1979 Richard Statman proved, using proof-theory, that the purely implicational fragment of Intuitionistic Logic (M→) is PSPACEcomplete. He showed a polynomially bounded translation from full Intuitionistic Propositional Logic into its implicational fragment. By the PSPACE-completeness of S4, proved by Ladner, and the Gödel translation from S4 into Intuitionistic Logic, the PSPACE-completenes...

In previous work, we have developed a “Glance-Look” model, which has replicated a broad profile of data on the semantic Attentional Blink (AB) task and characterized how attention deployment is modulated by emotion. The model relies on a distinction between two levels of meaning: implicational and propositional, which are supported by two corresponding mental subsystems. The somatic contributio...

This study examines the interacting roles of implicational markedness and frequency from the joint perspectives of formal linguistic theory, phonological acquisition and computational modeling. The hypothesis that child grammars are rankings of universal constraints, as in Optimality Theory (Prince & Smolensky, 1993/2004), that learning involves a gradual transition from an unmarked initial sta...

Conceptual Graphs (CG), originally developed for static data representation have been extended to cope with dynamical aspects. This paper adresses two questions connected with the topic: How can implicational knowledge about a system's states and behaviour be derived from a dynamic CG description and how can the CG speci cation process be supported by automatic or semiautomatic algorithms? Base...

We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is defined in terms of a threshold on a conditional probability of the consequent, given the antecedent: we are dealing with what the data analysis community c...

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...

In this paper we investigate the size of the fraction of tautologies of the given length n against the number of all formulas of length n for implicational logic. We are specially interested in asymptotic behavior of this fraction. We demonstrate the relation between a number of premises of implicational formula and asymptotic probability of finding formula with this number of premises. Further...

This is because the former are lexically implicated or entailed, and thus are more available and less expensive than the latter in the sense that they involve less practical reasoning. In addition, in terms of the strong-weak distinction, an implicational universal can be posited, namely that if a language has strong resultatives, it must have weak resultatives as well (Washio 1999, 2002). Seco...