Randomized Game Semantics for Semi-fuzzy Quantifiers

A propositional proof system is weakly automatizable if there is a polynomial time algorithm that separates satisfiable formulas from formulas that have a short refutation in the system, with respect to a given length bound. We show that if the resolution proof system is weakly automatizable, then parity games can be decided in polynomial time. We give simple proofs that the same holds for depth-1 propositional calculus (where resolution has depth 0) with respect to mean payoff and simple stochastic games. We define a new type of combinatorial game and prove that resolution is weakly automatizable if and only if one can separate, by a set decidable in polynomial time, the games in which the first player has a positional winning strategy from the games in which the second player has a positional winning strategy. Our main technique is to show that a suitable weak bounded arithmetic theory proves that both players in a game cannot simultaneously have a winning strategy, and then to translate this proof into propositional form. Database: ACM Digital Library 8 Title: Preferred First-Order Answer Set Programs Author: Vernon Asuncion, Yan Zhang, Yi Zhou Journal: ACM Transactions on Computational Logic, Volume 15 Issue 2, April 2014, Article No. 11 Abstract: In this article, we consider the issue of how first-order answer set programs can be extended for handling preference reasoning. To this end, we propose a progression-based preference semantics for first-order answer set programs while explicit preference relations are presented. We study essential properties of the proposed preferred answer set semantics. To understand the expressiveness of preferred first-order answer set programming, we further specify a second-order logic representation which precisely characterizes the progression-based preference semantics. Database: ACM Digital Library 9 Title: Linearity: A Roadmap Author: Sandra Alves, Maribel Fernández, Mário Florido, and Ian Mackie Journal: Journal of Logic and Computation, Volume 24 Issue 3 June 2014, Pp. 513-529 Abstract: In this article we discuss three different notions of linearity: syntactical, operational and denotational. We briefly define each notion of linearity, pointing out some of the main results in the area, and describe applications of linear languages and type systems. Database: Oxford Journals Online 10 Title: The enriched effect calculus: syntax and semantics Author: Jeff Egger, Rasmus Ejlers Møgelberg, and Alex Simpson Journal: Journal of Logic and Computation, Volume 24 Issue 3 June 2014, Pp. 615-654 Abstract: This article introduces the enriched effect calculus, which extends established type theories for computational effects with primitives from linear logic. The new calculus provides a formalism for expressing linear aspects of computational effects; e.g. the linear usage of imperative features such as state and/or continuations. This article introduces the enriched effect calculus, which extends established type theories for computational effects with primitives from linear logic. The new calculus provides a formalism for expressing linear aspects of computational effects; e.g. the linear usage of imperative features such as state and/or continuations. The enriched effect calculus is implemented as an extension of a basic effect calculus without linear primitives, which is closely related to Moggi's computational metalanguage, Filinski's effect PCF and Levy's call-by-push-value. We present syntactic results showing: the fidelity of the behaviour of the linear connectives of the enriched effect calculus; the conservativity of the enriched effect calculus over its non-linear core (the effect calculus); and the non-conservativity of intuitionistic linear logic when considered as an extension of the enriched effect calculus. The second half of the article investigates models for the enriched effect calculus, based on enriched category theory. We give several examples of such models, relating them to models of standard effect calculi (such as those based on monads), and to models of intuitionistic linear logic. We also prove soundness and completeness. Database: Oxford Journals Online