Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

A Polynomial Reduction of Forks Into Logic Programs

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG[Abstract] In this research note we present additional results for an earlier published paper [1]. There, we studied the problem of projective strong equivalence (PSE) of logic programs, that is, checking whether two logic programs (or propositional formulas) have the same behaviour (under the stable model semantics) regardless of a common context and ignoring the effect of local auxiliary atoms. PSE is related to another problem called strongly persistent forgetting that consists in keeping a program’s behaviour after removing its auxiliary atoms, something that is known to be not always possible in Answer Set Programming. In [1], we introduced a new connective ‘|’ called fork and proved that, in this extended language, it is always possible to forget auxiliary atoms, but at the price of obtaining a result containing forks. We also proved that forks can be translated back to logic programs introducing new hidden auxiliary atoms, but this translation was exponential in the worst case. In this note we provide a new polynomial translation of arbitrary forks into regular programs that allows us to prove that brave and cautious reasoning with forks has the same complexity as that of ordinary (disjunctive) logic programs and paves the way for an efficient implementation of forks. To this aim, we rely on a pair of new PSE invariance properties.We wish to thank the anonymous reviewers for their useful suggestions that have helped to improve the paper. This work was partially supported by MICINN, Spain, grant PID2020-116201GB-I00, Xunta de Galicia, Spain, grant GPC ED431B 2019/03, Universidade da Coruña/CISUG, Spain, (funding for open access charge) and National Science Foundation, USA, grant NSF Nebraska EPSCoR 95-3101-0060-402Xunta de Galicia; ED431B 2019/03USA. National Science Foundation; EPSCoR 95-3101-0060-40

Varieties of Linguistic Economy. Essays on Scope and Binding

The main body of the thesis is divided in three parts, each comprising two chapters. In the first part, I address the notion of scope from the perspective of linguistic economy, by discussing the drawbacks of an economy-based account of scope, and then I put forward an alternative account. In the second part, I apply a similar strategy, this time, with respect to binding. In the third part, I explore the theoretical consequences of the standard economy principles for two theses concerning, respectively, the nature of complex demonstratives and the purported logicality of natural language

08271 Abstracts Collection -- Topological and Game-Theoretic Aspects of Infinite Computations

From June 29, 2008, to July 4, 2008, the Dagstuhl Seminar 08271 ``Topological and Game-Theoretic Aspects of Infinite Computations\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, many participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available