Linear logic (LL) [9], [10](see Appendix A, B) is the logical foundation of some typetheoretic languages and also of environments for specification and theorem proving. In this paper, we consider the Multiplicative fragment of Linear Logic (MLL) from an automated deduction point of view. We propose an automated deduction (Automatic Proof Nets Construction and its implementation) based on the no...

Reasoning about programs is mostly deduction: the reasoning from the abstract model to the concrete run. Deduction is useful because it allows us to predict properties of future runs—up to the point that a program will never fail its specification. However, even such a 100% correct program may still show a problem: the specification itself may be problematic, or deduction required us to abstrac...

When defined with general elimination/application rules, natural deduction and λ-calculus become closer to sequent calculus. In order to get real isomorphism, normalisation has to be defined in a “multiary” variant, in which reduction rules are necessarily non-local (reason: nomalisation, like cut-elimination, acts at the head of applicative terms, but natural deduction focuses at the tail of s...

By taking into accountsome texts publishedbetweenthe first and the second edition of the Critique of Pure Reason that have been neglected by most of those who have dealt with the deductionof the categories, I argue that the core of the deduction is to be identified as the ‘almost single inference from the precisely determineddefinition of a judgment in general’, which Kant adumbrates in the Met...

In this paper, general logic-systems and a necessary and sufficient algorithm AG are used to substantiate significant consequence operator properties. It is shown, among other results, that, in certain cases, (1) if the number of steps in a deduction is restricted, then such deduction does not yield a consequence operator. (2) In general, for any non-organized infinite language L, there is a sp...

We present the certifying part of the Zenon Modulo automated theorem prover, which is an extension of the Zenon tableau-based first order automated theorem prover to deduction modulo. The theory of deduction modulo is an extension of predicate calculus, which allows us to rewrite terms as well as propositions, and which is well suited for proof search in axiomatic theories, as it turns axioms i...

The so called “cogen approach” to program specialisation, writing a compiler generator instead of a specialiser, has been used with considerable success in partial evaluation of both functional and imperative languages. This paper demonstrates that this approach is also applicable to partial evaluation of logic programming languages, also called partial deduction. Self-application has not been ...

The so called frame axioms problem or frame problem is well-known to anybody who is interested in automatic problem solving.Some information concerning this problem can be found in (1) or (2).In (2) the author proposes to eliminate the frame axioms in such a way that they are replaced by a new deduction rule denoted as UNLESS-operator.In fact,this operator is a rule enabling to derive that some...

There are recent successes of automated deduction techniques in various application domains, such as mathematics, classical and nonmonotonic logics, diagnosis, planning and within software engineering. We will briefly review some of them and observe that these successes have been made only after a careful analysis of the application domain as well as the deduction system under consideration. Th...