1,249 research outputs found
Scaled Boolean Algebras
Scaled Boolean algebras are a category of mathematical objects that arose
from attempts to understand why the conventional rules of probability should
hold when probabilities are construed, not as frequencies or proportions or the
like, but rather as degrees of belief in uncertain propositions. This paper
separates the study of these objects from that not-entirely-mathematical
problem that motivated them. That motivating problem is explicated in the first
section, and the application of scaled Boolean algebras to it is explained in
the last section. The intermediate sections deal only with the mathematics. It
is hoped that this isolation of the mathematics from the motivating problem
makes the mathematics clearer.Comment: 53 pages, 8 Postscript figures, Uses ajour.sty from Academic Press,
To appear in Advances in Applied Mathematic
Dual Logic Concepts based on Mathematical Morphology in Stratified Institutions: Applications to Spatial Reasoning
Several logical operators are defined as dual pairs, in different types of
logics. Such dual pairs of operators also occur in other algebraic theories,
such as mathematical morphology. Based on this observation, this paper proposes
to define, at the abstract level of institutions, a pair of abstract dual and
logical operators as morphological erosion and dilation. Standard quantifiers
and modalities are then derived from these two abstract logical operators.
These operators are studied both on sets of states and sets of models. To cope
with the lack of explicit set of states in institutions, the proposed abstract
logical dual operators are defined in an extension of institutions, the
stratified institutions, which take into account the notion of open sentences,
the satisfaction of which is parametrized by sets of states. A hint on the
potential interest of the proposed framework for spatial reasoning is also
provided.Comment: 36 page
Da linguĂstica gerativa Ă gramática categorial : sujeitos lexicais em infinitivos controlados
Orientadores: Marcelo Esteban Coniglio, Sonia Maria Lazzarini CyrinoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e CiĂŞncias HumanasResumo: A presente tese situa-se na interface da lĂłgica e da linguĂstica; o seu objeto de estudo sĂŁo os pronomes lexicais em sentenças de controle em trĂŞs lĂnguas Românicas: PortuguĂŞs, Italiano e Espanhol. Esse assunto tem recebido mais atenção na linguĂstica gerativa, especialmente nos anos recentes, do que na gramática de cunho lĂłgico. Talvez como consequĂŞncia disso, há ainda muito a ser entendido sobre essas estruturas linguĂsticas e as suas propriedades lĂłgicas. Essa tese tenta preencher as lacunas na literatura \--- ou, pelo menos, avançar nessa direção \--- colocando questões que nĂŁo foram suficientemente exploradas atĂ© agora. Para tal efeito avançamos duas perguntas-chaves, uma linguĂstica e a outra lĂłgica. Elas sĂŁo, respectivamente: Qual Ă© o estatuto sintático dos pronomes lexicais em estruturas de controle? E: Quais sĂŁo os mecanismos disponĂveis, em uma gramática lĂłgica livre de contração, para se reusar recursos semânticos? A tese divide-se, consequentemente, em duas partes: linguĂstica gerativa e gramática categorial. Na Parte I revisamos algumas das principais teorias de controle gerativistas e a recente discussĂŁo acerca das cláusulas infinitivas com sujeito lexical. Na Parte II revisamos a literatura categorial, atendendo principalmente Ă s propostas acerca das estruturas de controle e dos pronomes anafĂłricos. Em Ăşltima instância, mostraremos que as propostas linguĂsticas e lĂłgicas prĂ©vias precisam ser modificadas para se explicar o fenĂ´meno linguĂstico em questĂŁo. Com efeito, nos capĂtulos finais de cada uma das partes avançamos propostas alternativas que, a nosso ver, resultam mais adequadas que as suas rivais. Mais especĂficamente, na Parte I avançamos uma proposta linguĂstica na linha do cálculo de controle T/Agr de Landau. Na Parte II apresentamos duas propostas categoriais, uma na linha do cálculo categorial combinatĂłrio e a outra, na gramática lĂłgica de tipos. Finalmente mostramos a implementação da Ăşltima proposta em um analisador sintático e de demonstração categorialAbstract: The present thesis lies at the interface of logic and linguistics; its object of study are control sentences with overt pronouns in Romance languages (European and Brazilian Portuguese, Italian and Spanish). This is a topic that has received considerably more attention on the part of linguists, especially in recent years, than from logicians. Perhaps for this reason, much remains to be understood about these linguistic structures and their underlying logical properties. This thesis seeks to fill the lacunas in the literature \--- or at least take steps in this direction \--- by way of addressing a number of issues that have so far been under-explored. To this end we put forward two key questions, one linguistic and the other logical. These are, respectively: What is the syntactic status of the surface pronoun? And: What are the available mechanisms to reuse semantic resources in a contraction-free logical grammar? Accordingly, the thesis is divided into two parts: generative linguistics and categorial grammar. Part I starts by reviewing the recent discussion within the generative literature on infinitive clauses with overt subjects, paying detailed attention to the main accounts in the field. Part II does the same on the logical grammar front, addressing in particular the issues of control and of anaphoric pronouns. Ultimately, the leading accounts from both camps will be found wanting. The closing chapter of each of Part I and Part II will thus put forward alternative candidates, that we contend are more successful than their predecessors. More specifically, in Part I we offer a linguistic account along the lines of Landau's T/Agr theory of control. In Part II we present two alternative categorial accounts: one based on Combinatory Categorial Grammar, the other on Type-Logical Grammar. Each of these accounts offers an improved, more fine-grained perspective on control infinitives featuring overt pronominal subjects. Finally, we include an Appendix in which our type-logical proposal is implemented in a categorial parser/theorem-prover (categorial
parser/theorem-prover)DoutoradoFilosofiaDoutora em Filosofia2013/08115-1, 2015/09699-2FAPESPCAPE
A view of canonical extension
This is a short survey illustrating some of the essential aspects of the
theory of canonical extensions. In addition some topological results about
canonical extensions of lattices with additional operations in finitely
generated varieties are given. In particular, they are doubly algebraic
lattices and their interval topologies agree with their double Scott topologies
and make them Priestley topological algebras.Comment: 24 pages, 2 figures. Presented at the Eighth International Tbilisi
Symposium on Language, Logic and Computation Bakuriani, Georgia, September
21-25 200
The Logic of Partitions: Introduction to the Dual of the Logic of Subsets
Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms--which is reflected in the duality between quotient objects and subobjects throughout algebra. Modern categorical logic as well as the Kripke models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic might be the logic of subsets of a given universe set. If "propositional" logic is thus seen as the logic of subsets of a universe set, then the question naturally arises of a dual logic of partitions on a universe set. This paper is an introduction to that logic of partitions dual to classical subset logic. The paper goes from basic concepts up through the correctness and completeness theorems for a tableau system of partition logic
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