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Kleene Algebras, Regular Languages and Substructural Logics [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We introduce the two substructural propositional logics KL, KL+ , which use disjunction, fusion and a unary, (quasi-)exponential connective. For both we prove strong completeness with respect to the interpretation in Kleene algebras and a variant thereof.
Christian Wurm
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Stone-Type Dualities for Separation Logics [PDF]
Logical Methods in Computer Science, 2019 Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence, yielding a ...
Simon Docherty, David Pym
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Convolution Algebras: Relational Convolution, Generalised Modalities and Incidence Algebras [PDF]
Logical Methods in Computer Science, 2021 Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of relational convolution
Brijesh Dongol +2 more
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Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics
Axioms, 2021 Recently, algebraic Routley–Meyer-style semantics was introduced for basic substructural logics. This paper extends it to fuzzy logics. First, we recall the basic substructural core fuzzy logic MIAL (Mianorm logic) and its axiomatic extensions, together ...
Eunsuk Yang
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Why a Logic is not only its Set of Valid Inferences
Análisis Filosófico, 2021 The main idea that we want to defend in this paper is that the question of what a logic is should be addressed differently when structural properties enter the game.
Eduardo A. Barrio, Federico Pailos
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Structural Rules in Natural Deduction with Alternatives
Bulletin of the Section of Logic, 2023 Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives.
Greg Restall
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Outline of a Dialogical Theory of Truth
Crítica, 2023 In this essay I propose two theories of truth and show how they deal with semantic paradoxes. Their most salient feature is that they are based on a gametheoretic understanding of logic and meaning.
Miguel Álvarez Lisboa
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Command injection attacks, continuations, and the Lambek calculus [PDF]
Electronic Proceedings in Theoretical Computer Science, 2016 This paper shows connections between command injection attacks, continuations, and the Lambek calculus: certain command injections, such as the tautology attack on SQL, are shown to be a form of control effect that can be typed using the Lambek calculus,
Hayo Thielecke
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Duality Theory and Categorical Universal Logic: With Emphasis on Quantum Structures [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical, intuitionistic, and ...
Yoshihiro Maruyama
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Local Search and the Evolution of World Models
Topics in Cognitive Science, EarlyView., 2023 Abstract An open question regarding how people develop their models of the world is how new candidates are generated for consideration out of infinitely many possibilities. We discuss the role that evolutionary mechanisms play in this process. Specifically, we argue that when it comes to developing a global world model, innovation is necessarily ...
Neil R. Bramley +3 more
wiley +1 more source