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Sequent Calculus Viewed Modulo
 University of Birmingham
, 2000
"... The firstorder sequent calculus is generally considered as containing no computation but only pure deduction. But this is not completely true if we look at it carefully, using a deduction modulo framework. The origins of the computational part are first implicit behaviours of the calculus, then wel ..."
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The firstorder sequent calculus is generally considered as containing no computation but only pure deduction. But this is not completely true if we look at it carefully, using a deduction modulo framework. The origins of the computational part are first implicit behaviours of the calculus
A Sequent Calculus for Circumscription
, 1997
"... . In this paper, we introduce a sequent calculus CIRC for propositional Circumscription. This work is part of a larger project, aiming at a uniform prooftheoretic reconstruction of the major families of nonmonotonic logics. Among the novelties of the calculus, we mention that CIRC is analytic ..."
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. In this paper, we introduce a sequent calculus CIRC for propositional Circumscription. This work is part of a larger project, aiming at a uniform prooftheoretic reconstruction of the major families of nonmonotonic logics. Among the novelties of the calculus, we mention that CIRC is analytic
Adventures in Sequent Calculus Modulo Equations
, 1998
"... We apply the notion of an oriented rewrite theory and the associated coherence techniques in order to develop a framework for theorem proving modulo equations. This is achieved using existing rewriting techniques and a few simple lemmas, and is intended to serve as a case study of the use of an orie ..."
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We apply the notion of an oriented rewrite theory and the associated coherence techniques in order to develop a framework for theorem proving modulo equations. This is achieved using existing rewriting techniques and a few simple lemmas, and is intended to serve as a case study of the use
Completeness of CutFree Sequent Calculus Modulo
"... Abstract. Deduction modulo is a powerful way to replace axioms by rewrite rules and allows to integrate computation in deduction. But adding rewrite rules is not always safe for properties of the deduction system such as consistency or cut elimination. Proving completeness of the cutfree calculus w ..."
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and techniques that lead to the cut elimination theorem for the classical sequent calculus modulo. At last, we give a rewrite rule featuring cutelimination, but nonnormalizing.
Automating Theories in Intuitionistic Logic
 in "7th International Symposium on Frontiers of Combining Systems FroCoSâ€™09, Italie
"... Abstract. Deduction modulo consists in applying the inference rules of a deductive system modulo a rewrite system over terms and formulĂ¦. This is equivalent to proving within a socalled compatible theory. Conversely, given a firstorder theory, one may want to internalize it into a rewrite system t ..."
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be transformed into a rewrite system with an analytic sequent calculus modulo is not corecursively enumerable. We nonetheless propose a procedure to transform a large class of theories into compatible rewrite systems. We then extend this class by working in conservative extensions, in particular using
A Sequent Calculus for Signed Interval Logic
, 2001
"... We propose and discuss a complete sequent calculus formulation for Signed Interval Logic (SIL) with the chief purpose of improving proof support for SIL in practice. The main theoretical result is a simple characterization of the limit between decidability and undecidability of quantifierfree SIL. ..."
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We propose and discuss a complete sequent calculus formulation for Signed Interval Logic (SIL) with the chief purpose of improving proof support for SIL in practice. The main theoretical result is a simple characterization of the limit between decidability and undecidability of quantifierfree SIL
Results 1  10
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