Natural deduction is a logical system that closely mimics the natural human reasoning process, using not axioms but rather assumptions that are made and later discharged when they are no longer needed. Logical proofs like these, however, lack the ability to handle varying levels of uncertainty and the contradictions that may arise when they are applied to real world situations. The goal of the ...

This paper describes a logical design process model and in particular abduction in it. We present our model of design processes that consists of abduction, deduction, circumscription, meta-level inference, and multi-world mechanism. In this model, design is a process of re ning descriptions of design objects. Abduction generates object descriptions as a hypothesis, deduction examines validity o...

Logical inferentialism claims that the meaning of the logical constants should be given, not model-theoretically, but by the rules of inference of a suitable calculus. It has been claimed that certain proof-theoretical systems, most particularly, labelled deductive systems for modal logic, are unsuitable, on the grounds that they are semantically polluted and suffer from an untoward intrusion o...

Recent work has seen the emergence of a common framework for parsing categorial grammar (CG) formalisms that fall within the 'type-logical' tradition (such as the Lambek calculus and related systems), whereby some method of linear logic theorem proving is used in combination with a system of labelling that ensures only deductions appropriate to the relevant grammatical logic are allowed. The ap...

One hypothesis is more general than another one if it covers all instances that are also covered by the later one. The former hypothesis is called a generalization of the later, and the later a specialization of the former. When using logical formulae as hypotheses, the generality relation coincides with the notion of logical entailment, which implies that the generality relation can be analyze...

In this paper we consider the problem of deriving a term assignment system for Girard's Intuitionistic Linear Logic for both the sequent calculus and natural deduction proof systems. Our system di ers from previous calculi (e.g. that of Abramsky [1]) and has two important properties which they lack. These are the substitution property (the set of valid deductions is closed under substitution) a...

Deduction modulo is an extension of first-order predicate logic where axioms are replaced by a congruence relation on propositions and where many theories, such as arithmetic, simple type theory and some variants of set theory, can be expressed. An important question in deduction modulo is to find a condition of the theories that have the strong normalization property. Dowek and Werner have giv...

In this paper, we show how an appropriate possible world semantics exhibits the fundamental diierences between various forms of logical reasoning such as deduction, abduction and induction. The ensuing model theoretic formal-isation provides a solid foundation for exact further discourse on the issue, such as deciding whether a particular instance of reasoning should be classiied as abduction o...

We introduce a method to associate calculi of proof terms and rewrite rules with cut elimination procedures for logical deduction systems (i.e., Gentzen-style sequent calculi) in the case of intuitionistic logic. We illustrate this method using two different versions of the cut rule for a variant of the intuitionistic fragment of Kleene's logical deduction system G3. Our systems are in fact cal...