1,198 research outputs found

    Stationary logic of finitely determinate structures

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    AbstractIn this part we develop the theory of finitely determinate structures, that is, structures on which the dual quantifiers “stat” and “unreadable” have the same meaning. Among other genera

    The Grail theorem prover: Type theory for syntax and semantics

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    As the name suggests, type-logical grammars are a grammar formalism based on logic and type theory. From the prespective of grammar design, type-logical grammars develop the syntactic and semantic aspects of linguistic phenomena hand-in-hand, letting the desired semantics of an expression inform the syntactic type and vice versa. Prototypical examples of the successful application of type-logical grammars to the syntax-semantics interface include coordination, quantifier scope and extraction.This chapter describes the Grail theorem prover, a series of tools for designing and testing grammars in various modern type-logical grammars which functions as a tool . All tools described in this chapter are freely available

    Model theory in compactly generated (tensor-)triangulated categories

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    We give an account of model theory in the context of compactly generated triangulated and tensor-triangulated categories T{\cal T}. We describe pp formulas, pp-types and free realisations in such categories and we prove elimination of quantifiers and elimination of imaginaries. We compare the ways in which definable subcategories of T{\cal T} may be specified. Then we link definable subcategories of T{\cal T} and finite-type torsion theories on the category of modules over the compact objects of T{\cal T}. We briefly consider spectra and dualities. If T{\cal T} is tensor-triangulated then new features appear, in particular there is an internal duality in rigidly-compactly generated tensor-triangulated categories

    The prospects for mathematical logic in the twenty-first century

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    The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.Comment: Association for Symbolic Logi

    On the Computational Complexity of Information Hiding

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    In this work we study the intrinsic complexity of elimination algorithms in effective algebraic geometry and we focus our attention to elimination algorithms produced within the object–oriented paradigm. To this end, we describe a new computation model called quiz game (introduced in [1]) which models the notions of information hiding (due to Parnas, see [2]) and non–functional requirements (e.g. robustness) among other important concepts in software engineering. This characteristic distinguish our model from classical computation models such as the Turing machine or algebraic models. We illustrate our computation model with a non–trivial complexity lower bound for the identity function of polynomials. We show that any object–oriented (and robust) implementation of the identity function of polynomials is necessarily inefficient compared with a trivial implementation of this function. This result shows an existing synergy between Software Engineering and Algebraic Complexity Theory.Sociedad Argentina de Informática e Investigación Operativa (SADIO
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