1,198 research outputs found
Stationary logic of finitely determinate structures
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
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
We give an account of model theory in the context of compactly generated
triangulated and tensor-triangulated categories . 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 may be specified. Then we link
definable subcategories of and finite-type torsion theories on the
category of modules over the compact objects of . We briefly consider
spectra and dualities. If 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
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
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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