2 Natural Deduction and Sequent Calculus 1 2.1 Natural Deduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 Sequent Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.3 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

This report documents the program and the outcomes of Dagstuhl Seminar 15381 “Information from Deduction: Models and Proofs”. The aim of the seminar was to bring together researchers working in deduction and applications that rely on models and proofs produced by deduction tools. Proofs and models serve two main purposes: (1) as an upcoming paradigm towards the next generation of automated dedu...

Title Type automated deduction cade 22 22nd international conference on automated deduction montreal canada PDF automated deduction cade 21 21st international conference on automated deduction bremen germany PDF logic programming and automated reasoning 6th international conference lpar99 tbilisi georgia s PDF automated technology for verification and analysis second international conference at...

We present in this paper a new type system which allows to extract code for an abstract machine instead of lambda-terms. Thus, we get a framework to compile correctly programs extracted from proof by translating their proof in our system and then extracting the code. Moreover, we will see that we can associate programs to classical proofs.

In this paper we give a natural deduction formulation of hybrid logic. Our natural deduction system can be extended with additional inference rules corresponding to conditions on the accessibility relations expressed by so-called geometric theories. Thus, we give natural deduction systems in a uniform way for a wide class of hybrid logics which appears to be impossible in the context of ordinar...

In this paper we argue that sequent proofs systems are a better deductive apparatus for introducing proofs to students than are natural deduction systems. Natural deduction derivations of superintuitionistic theorems (theorems of classical logic that are not intuitionistically valid) require indirect and often obtuse constructions. Constructing derivations in sequent systems is uniform, driven ...

In a system of sequents for intuitionistic predicate logic a theorem, which corresponds to Prawitz’s Normal Form Theorem for natural deduction, are proved. In sequent derivations a special kind of cuts, maximum cuts, are defined. Maximum cuts from sequent derivations are connected with maximum segments from natural deduction derivations, i.e., sequent derivations without maximum cuts correspond...

Polarized conceptual graphs (PGs) are simple conceptual graphs added with a restricted form of negation, namely negation on relations. Classical deduction with PGs (in short PG-Deduction) is highly intractable; it is indeed Π P complete. In [LM06] a brute-force algorithm for solving PG-Deduction was outlined. In the present paper, we extend previous work with two kinds of results. First, we exh...

The notion of partial deduction known from logic programming is deened in the framework of Structural Synthesis of Programs (SSP). Partial deduction for unconditional computability statements in SSP is deened. Completeness and correctness of partial deduction in the framework of SSP are proven. Several tactics and stopping criteria are suggested.

In this paper, we show how a system for automated deduction can be given computational reeection, i.e. can aaect its own computation mechanism, by using the very same machinery implementing logical deduction. This feature, that we call computational reeection via mechanized logical deduction, provides both theoretical and practical advantages. First, the theorem prover can inspect, extend and m...