5 research outputs found

    Bounding Resource Consumption with Gödel-Dummett Logics

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    International audienceGödel-Dummett logic LC and its finite approximations LCn are the intermediate logics complete w.r.t. linearly ordered Kripke models. In this paper, we use LCn logics as a tool to bound resource consumption in some process calculi. We introduce a non-deterministic process calculus where the consumption of a particular resource denoted * is explicit and provide an operational semantics which measures the consumption of this resource.We present a linear transformation of a process P into a formula f of LC. We show that the consumption of the resource by P can be bounded by the positive integer n if and only if the formula f admits a counter-model in LCn. Combining this result with our previous results on proof and counter-model construction for LCn, we conclude that bounding resource consumption is (linearly) equivalent to searching counter-models in LCn

    Graph-based decision for Gödel-Dummett logics

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    International audienceWe present a graph-based decision procedure for Gödel-Dummett logics and an algorithm to compute counter-models. A formula is transformed into a conditional bi-colored graph in which we detect some specific cycles and alternating chains using matrix computations. From an instance graph containing no such cycle (resp. no (n+1)-alternating chain) we extract a counter-model in LC (resp. LCn)

    Automated Reasoning

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    This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

    Bounding Resource Consumption with Gödel-Dummett Logics

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    Gödel-Dummett logic LC and its finite approximations LCn are the intermediate logics complete w.r.t. linearly ordered Kripke models. In this paper, we use LCn logics as a tool to bound resource consumption in some process calculi. We introduce a non-deterministic process calculus where the consumption of a particular resource denoted • is explicit and provide an operational semantics which measures the consumption of this resource. We present a linear transformation of a process P into a formula f of LC. We show that the consumption of the resource by P can be bounded by the positive integer n if and only if the formula f admits a counter-model in LCn. Combining this result with our previous results on proof and counter-model construction for LCn, we conclude that bounding resource consumption is (linearly) equivalent to searching counter-models in LCn

    The Persistence of Minimalism

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    The following work develops a new and general theory of minimalism – one addressing both its transhistorical and interdisciplinary dimensions, and capable of accounting for existing minimalism of every epoch and in every medium, while suitably open to embrace minimalist work yet to be created. To offer such a theory it is necessary not only to revisit the histories of minimalist practice and criticism, but also to consider its radical philosophical ground and implications. Hence its principal thesis – that minimalism exemplifies the persistence and facticity of the Real – grapples at once with the ontological heart of minimalist theory, and its practical instantiation through canonical as well as rarely considered examples. Divided into three parts, the first part addresses minimalism as the manifestation of particular aesthetic properties in relation to critical and theoretical trends. Since it becomes apparent that no single descriptive or theoretical account adequately frames minimalism, the discussion turns to the possibility of discovering a philosophical ground equally radical to the minimalist objects it addresses. The Real – an indifferent field of forces from which contingent entities are subtracted from within an irreversible temporal passage – offers precisely this radical continuum. Minimalism, by exposing the continuity between radical poiesis and an essentially quantitative understanding of Being, clarifies the indifferent persistence of the Real in every existential situation. Penetrating to the heart of this proposition, parts two and three respectively address minimalism in terms of its quantitative logic of Being – every exemplary subtraction from which is instantiated a type of existential calculation – and its exemplary aesthetic manifestation in terms of an existential transumption – a constructive poietic displacement by which minimalism renders itself maximally intelligible in terms of its objecthood and persistence. The work concludes with a typology which reorients and confirms the substance of the preceding argumentation
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