This paper provides a logical basis for manipulation with fuzzy IF-THEN rules. Our theory is wide enough and it encompasses not only finding a conclusion by means of the compositional rule of inference due to Lotfi A. Zadeh but also other kinds of approximate reasoning methods, e.g. perception-based deduction, provided that there exists a possibility to characterize them within a formal logical...

Natural Deduction style presentations of program logics are useful in view of the implementation of such logics in interactive proof development environments, based on type theory, such as LEGO, Coq, etc. In fact, ND-style systems are the kind of systems which can take best advantage of the possibility of reasoning “under assumptions” offered by proof assistants generated by Logical Frameworks....

Based on natural deduction, Pure Type Systems (PTS) can express a wide range of type theories. In order to express proof-search in such theories, we introduce the Pure Type Sequent Calculi (PTSC) by enriching a sequent calculus due to Herbelin, adapted to proof-search and strongly related to natural deduction. PTSC are equipped with a normalisation procedure, adapted from Herbelin’s and defined...

1. Introduction. The purpose of this paper is to present a theory of in-ductive inference and rational acceptance in scientific inquiry. A concept of relevant deduction is defined in which the truth of each and every premise of a deductive argument is essential to establishing the truth of the conclusion by deduction from the premises. This definition is based on the completely abstract notion ...

The present paper consists in a reconstruction of the notions recognition Schiller’s Letter on Aesthetic Education, Schelling’s New Deduction Natural Law and Fichte’s Foundations Law. focusses logical dynamics these authors employ when they explain interaction between intersubjectivity subjectivity meaning concept freedom acquires each account recognition.

ELAN is a powerful language and environment for specifying and prototyping deduction systems in a language based on rewrite rules controlled by strategies. It offers a natural and simple logical framework for the combination of the computation and deduction paradigms. It supports the design of theorem provers, logic programming languages, constraint solvers and decision procedures. ELAN takes f...

The aim of this paper is to show that a restriction of a logical language to clauses like Horn clauses, as they are used in Prolog, applied to 0,1]{valued logics leads to calculi with a sound and complete proof theory. In opposition to other models where generally the set of axioms as well as the deduction schemata are enriched we restrict ourselves to a simple modiication of the deduction rule...

We present a sequent calculus for intuitionistic non-commutative linear logic (INCLL), show that it satisfies cut elimination, and investigate its relationship to a natural deduction system for the logic. We show how normal natural deductions correspond to cut-free derivations, and arbitrary natural deductions to sequent derivations with cut. This gives us a syntactic proof of normalization for...

Rewriting logic is a well-known logic that emerged as an adequate logical and semantic framework for the specification of languages and systems. ρLog is a calculus for rule-based programming with labeled rules. Its expressive power stems from the usage of a fragment of higher-order logic (e.g., sequence variables, and function variables) to express atomic formulas. Its adequacy as a computation...