We study a higher order uniication procedure based on proof nets. In this paper, we present higher order uniication algorithm for intuitionistic implicational multiplicative fragment of proof nets and show termination and soundness for the algorithm.

We present a semantics (using Kripke lambda models) for a logical framework (minimal implicational predicate logic with quantiication over all higher types). We apply the semantics to obtain straightforward adequacy proofs for encodings of logics in the framework.

The formalism of GUHA style data mining is confronted with the approach of relational structures of D untsch, Orlowska and others. A computational complexity result on tautologies with implicational quan-tiiers is presented.

A general -observation-basedqualitative framework to extract agent-based pedestrian behavior is presented. To extract qualitative rules from data we use tools, from Formal Concept Analysis, for implicational reasoning.

We present a system of natural deduction and associated term calculus for intuitionistic non-commutative linear logic (INCLL) as a conservative extension of intuitionistic linear logic. We prove subject reduction and the existence of canonical forms in the implicational fragment.

The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)’s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Lukasiewicz, modal logics that admit the ru...

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...