CEDRIC - cpr RSS feedfrFri, 08 Jul 2011 15:42:49 +0200http://cedric.cnam.fr/index.php/publis/article/view?id=2094
http://cedric.cnam.fr/index.php/publis/article/view?id=2094
Paper - Structural Analysis of Narratives with the Coq Proof Assistant. This paper proposes a novel application of Interactive Proof
Assistants for studying the formal properties of Narratives, building on
recent work demonstrating the suitability of Intuitionistic Linear Logic
as a conceptual model. More specifically, we describe a method for mod-
elling narrative resources and actions, together with constraints on the
story endings in the form of an ILL sequent. We describe how well-formed
narratives can be interpreted from cut-free proof trees of the sequent ob-
tained using Coq. We finally describe how to reason about narratives at
the structural level using Coq: by allowing one to prove 2nd order prop-
erties on the set of all the proofs generated by a sequent, Coq assists
the verification of structural narrative properties traversing all possible
variants of a given plot.
Mon, 04 Jul 2011 14:50:14 +0200CPRPaperhttp://cedric.cnam.fr/index.php/publis/article/view?id=2075
http://cedric.cnam.fr/index.php/publis/article/view?id=2075
Paper - Efficiently Simulating Higher-Order Arithmetic by a First-Order Theory ModuloIn deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the reasoning that is intrinsic of the theory does not appear in the length of proofs. In general, the congruence is defined through a rewrite system over terms and propositions. We define a rigorous framework to study proof lengths in deduction modulo, where the congruence must be computed in polynomial time. We show that even very simple rewrite systems lead to arbitrary proof-length speed-ups in deduction modulo, compared to using axioms. As higher-order logic can be encoded as a first-order theory in deduction modulo, we also study how to reinterpret, thanks to deduction modulo, the speed-ups between higher-order and first-order arithmetics that were stated by GÃ¶del. We define a first-order rewrite system with a congruence decidable in polynomial time such that proofs of higher-order arithmetic can be linearly translated into first-order arithmetic modulo that system. We also present the whole higher-order arithmetic as a first-order system without resorting to any axiom, where proofs have the same length as in the axiomatic presentation. Mon, 04 Jul 2011 14:49:35 +0200CPRPaper