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Orientador: Marcelo Esteban Coniglio / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas / Made available in DSpace on 2018-08-25T12:43:36Z (GMT). No. of bitstreams: 1 Peron_NewtonMarques_D.pdf: 1773917 bytes, checksum: da2d2a1b1ecf8da6e26e419dee4888c5 (MD5) Previous issue date: 2014 / Resumo: Esse é um estudo sobre a viabilidade de matrizes finitas como semântica para lógica modal. Separamos nossa análise em dois casos: matrizes determinísticas e não-determinísticas. No primeiro caso, generalizamos o Teorema de Incompletude de Dugundji, garantindo que uma vasta família de lógicas modais não pode ser caracterizada por matrizes determinísticas finitas. No segundo caso, ampliamos a semântica de matrizes não- determinísticas para lógica modal proposta independentemente por Kearns e Ivlev. Essa ampliação engloba sistemas modais que, de acordo com nossa generalização, não podem ser caracterizados por matrizes determinísticas finitas / Abstract: This is a study on the feasibility of finite matrices as semantics for modal logics. We separate our analysis into two cases: deterministic and non-deterministic matrices. In the first case, we generalize Dugundji's Incompleteness Theorem, ensuring that a wide family of modal logic cannot be characterized by deterministic finite matrices. In the second, we extend the non-deterministic matrices semantics to modal logics proposed independently by Kearns and Ivlev. This extension embraces modal systems that, according to our generalization, cannot be characterized by finite deterministic matrices / Doutorado / Filosofia / Doutor em Filosofia

A generalized inclusion (g.i.) frame consists of a set of points (or "worlds") W and an assignment of a binary relation Rw on W to each point w in W. generalized inclusion frames whose Rw are partial orders are called comparison frames. Conditional logics of various comparative notions, for example, Lewis's V-logic of comparative possibility and utilitarian accounts of conditional obligation, model the dyadic modal operator > on comparison frames according to (what amounts to) the following truth condition: oc>13"holds at w" if every point in the truth set of a bears Rw to some point where holds. In this essay I provide a relational frame theory which embraces both accessibility semantics and g.i. semantics as special cases. This goal is achieved via a philosophically significant generalization of universal strict implication which does not assume accessibility as a primitive. Within this very general setting, I provide the first axiomatization of the dyadic modal logic corresponding to the class of all g.i. frames. Various correspondences between dyadic logics and first order definable subclasses of the class of g.i. frames are established. Finally, some general model constructions are developed which allow uniform completeness proofs for important sublogics of Lewis' V. / Arts, Faculty of / Philosophy, Department of / Graduate

ModaI logic is concerned with the logic of necessity and possibility. The central problem of modal ontology is summed up in the following question, "What are the ontological commitments of the user of modal terminology? " This thesis is primarily about the ontological commitments that Aristotle made when he employed modal terms. Aristotle’s modal ontology is h e r e analysed in conjunction with four modal problems. My primary objective, is to clarify some of the discussions of Aristotle's modal ontology that have been advanced by certain twentieth century philosophers. The first problem to be considered is the famous ' sea battle’ argument of De Interpretatione 9 . Here is a summary of the problem: If it is currently true that there will be a sea battle tomorrow, then in some sense it is inevitable that there will in fact be a sea battle; if predictions are true, is not a form of determinism being supported? One analysis in particular is studied at length, namely that of Jaakko Hintikka. Hintikka holds that the sea battle argument is best Interpreted if the metaphysical principle of plenitude is attributed to Aristotle. The principle of plenitude effectively merges modality with temporality; what is necessarily the case is always true, and vice versa. Hintikka also interprets Aristotle's stand on the ‘Master Argument’ of Diodorus in light of the attribution of the principle of plenitude to Aristotle. Diodorus' argument is the second of the four problems that this essay considers,. Unlike Aristotle, Diodorus appears to have favored a strong version of determinism. According to Hintikka, Diodorus actually strove to prove the principle of plenitude (as opposed to assuming it, as Aristotle presumably did). I am very sceptical regarding Hintikka's interpretations of these two problems. The sea battle argument is not adequately answered by the solution which Hintikka sees Aristotle adopting. Alternative answers are relatively easy to come by. The evidence cited by Hintikka for ascribing the principle of plenitude is, it is shown, somewhat inconclusive. As for the Master Argument, there is a great deal of paucity in regards to textual evidence. Hinikka himself virtually concedes this point. (Thus, whereas I feel it to be incumbent to offer an alternative interpretation of the sea battle argument, I do not share this attitude towards the Master Argument.) The third and fourth problems play a key role in twentieth century analytic philosophy. Both were first formulated by W.V. Quine in the forties. These problems are somewhat subtle and will not be explained further. Suffice it to say that an analysis of Aristotle's works by Alan Code reveals that the Stagirite had an answer to Quine's criticisms of modal logic. / Arts, Faculty of / Philosophy, Department of / Graduate

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Ph.D. (Mathematics) / Algebraic methods have been largely ignored within the eld of hybrid logics. A main theme of this thesis is to illustrate the usefulness of algebraic methods in this eld. It is a well-known fact that certain properties of a logic correspond to properties of particular classes of algebras, and that we therefore can use these classes of algebras to answer questions about the logic. The rst aim of this thesis is to identify a class of algebras corresponding to hybrid logics. In particular, we introduce hybrid algebras as algebraic semantics for the better known hybrid languages in the literature. The second aim of this thesis is to use hybrid algebras to solve logical problems in the eld of hybrid logic. Specically, we will focus on proving general completeness results for some well-known hybrid logics with respect to hybrid algebras. Next, we study Sahlqvist theory for hybrid logics. We introduce syntactically de ned classes of hybrid formulas that have rst-order frame correspondents, which are preserved under taking Dedekind MacNeille completions of atomic hybrid algebras, and which are preserved under canonical extensions of permeated hybrid algebras. Finally, we investigate the nite model property (FMP) for several hybrid logics. In particular, we give analogues of Bull's theorem for the hybrid logics under consideration in this thesis. We also show that if certain syntactically de ned classes of hybrid formulas are added to the normal modal logic S4 as axioms, we obtain hybrid logics with the nite model property.

M.Sc.

In this paper, I begin to develop a theory called Paradise on the Cheap - in so doing, I intend to provide a rival to David Lewis' modal realism. Paradise on the Cheap grounds possibilia in the features of the actual world; and so, it does not require realist commitments to the existence of non-actual worlds and individuals. I explain modality, conterfactuals, content, and properties in terms of recombinations of actual-world features, second-order mathematical schemata, and the similarity relations which hold between these things and parts of the actual world. Because the ontology of Paradise on the Cheap promotes unity and economy of theory to a greater extent than does model realism's ontology, I argue that we should accept the former theory instead of the latter. Moreover, I address the question of whether inference to the best explanation is an argumentative strategy that is even available to modal realists. / vii, 141 leaves : ill. ; 28 cm.

Thesis (Ph. D.)--University of California, San Diego, 2008. / Title from first page of PDF file (viewed December 5, 2008). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 160-164).

Thesis (Master)--İzmir Institute of Technology, İzmir, 2006 / Keywords:Temporal logic, modal logic. Includes bibliographical references (leaves 45).