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The family of default logics formalize the default reasoning using nonmonotonic inference rules called defaults. In this paper we propose a uniform abstract characterization of credulous default inference associated to all versions (classical, justified, constrained, rational) of propositional default logic using the credulous default sequent calculi. These axiomatic systems combine sequent and anti-sequent...
We present a syntax for MALL (multiplicative additive linear logic without units) proof nets which refines Girard's one. It is also based on the use of monomial weights for identifying additive components (slices). Our generalization gives the possibility of representing a kind of sharing of nodes which does not exist in Girard's nets. This sharing leads to the definition of a strong cut elimination...
Variable binding is a prevalent feature of the syntax and proof theory of many logical systems. In this paper, we define a programming language that provides intrinsic support for both representing and computing with binding. This language is extracted as the Curry-Howard interpretation of a focused sequent calculus with two kinds of implication, of opposite polarity. The representational arrow extends...
In predicate logic, the proof that a theorem P holds in a theory Th is typically conducted in natural deduction or in the sequent calculus using all the information contained in the theory in a uniform way. Introduced ten years ago, deduction modulo allows us to make use of the computational part of the theory Th for true computations modulo which deductions are performed. Focusing on the sequent...
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