Artículos con la etiqueta ‘Lógica’

(In)dependence Logic and Abstract Independence Relations

Por • 30 ene, 2014 • Category: Opinion

We generalize the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a model-theoretic interpretation of the independence atom and characterize under which conditions we can prove a completeness result with respect to the deductive system that axiomatizes independence in team semantics.



Category theory, logic and formal linguistics: some connections, old and new

Por • 30 ene, 2014 • Category: Crítica

We seize the opportunity of the publication of selected papers from the \emph{Logic, categories, semantics} workshop in the \emph{Journal of Applied Logic} to survey some current trends in logic, namely intuitionistic and linear type theories, that interweave categorical, geometrical and computational considerations. We thereafter present how these rich logical frameworks can model the way language conveys meaning.



A report on Tarski’s decidability problem

Por • 29 ene, 2014 • Category: Educacion

This paper contains a list of crucial mistakes and counterexamples to some of the main statements in the paper “Elementary theory of free nonabelian groups” by O. Kharlampovich and A. Myasnikov, which was published in the Journal of Algebra in June 2006.



Extensionality of lambda-*

Por • 7 ene, 2014 • Category: Opinion

We prove an extensionality theorem for the “type-in-type” dependent type theory with Sigma-types. We suggest that the extensional equality type be identified with the logical equivalence relation on the free term model of type theory.



Internalization of extensional equality

Por • 7 ene, 2014 • Category: Crítica

In recent years, a number of researchers have suggested that the extensional equality in type theory is the canonical logical relation defined by induction on type structure (Tait [1998], Altenkirch et al [2008], Coquand [2010], Harper et al [2013]). Here we make this position explicit in the statement of Extensionality Thesis.



Information-theoretic interpretation of quantum formalism

Por • 6 ene, 2014 • Category: Leyes

We propose an information-theoretic interpretation of quantum formalism based on Bayesian probability and free from any additional axiom. Quantum information is construed as a technique of statistical estimation of the variables within an information manifold. We start from a classical register. The input data are converted into a Bayesian prior, conditioning the probability of the variables involved. In static systems, this framework leads to solving a linear programming problem which is next transcribed into a Hilbert space using the Gleason theorem. General systems are introduced in a second step by quantum channels. This provides an information-theoretic foundation to quantum information, including the rules of commutation of observables. We conclude that the theory, while dramatically expanding the scope of classical information, is not different from the information itself and is therefore a universal tool of reasoning.



Experimental library of univalent formalization of mathematics

Por • 5 ene, 2014 • Category: Ambiente

This paper contains a discussion of a library of formalized mathematics for the proof assistant Coq which the author worked on in 2011-13.



Defining implication relation for classical logic

Por • 5 ene, 2014 • Category: Opinion

Simple and useful classical logic is unfortunately defective with its problematic definition of material implication. This paper presents an implication relation defined by a simple equation to replace the traditional material implication in classical logic. Common “paradoxes” of material implication are avoided while simplicity and usefulness of the system are reserved with this implication relation.



Foundations of statistical inference, revisited

Por • 31 dic, 2013 • Category: Leyes

This is an invited contribution to the discussion on Professor Deborah Mayo’s paper, “On the Birnbaum argument for the strong likelihood principle,” to appear in Statistical Science. Mayo clearly demonstrates that statistical methods violating the likelihood principle need not violate either the sufficiency or conditionality principle, thus refuting Birnbaum’s claim. With the constraints of Birnbaum’s theorem lifted, we revisit issues related to the foundations of statistical inference, focusing on some new foundational principles, the inferential model framework, and connections with sufficiency and conditioning.



Arithmetical Foundations – Excerpt

Por • 31 dic, 2013 • Category: Crítica

Recursive maps, nowadays called primitive recursive maps, PR maps, have been introduced by G\”odel in his 1931 article for the arithmetisation, g\”odelisation, of metamathematics. For construction of his undecidable formula he introduces a non-constructive, non-recursive predicate beweisbar, provable. Staying within the area of categorical free-variables theory PR of primitive recursion or appropriate extensions opens the chance to avoid the two (original) G\”odel’s incompleteness theorems: these are stated for Principia Mathematica und verwandte Systeme, “related systems” such as in particular Zermelo-Fraenkel set theory ZF and v. Neumann G\”odel Bernays set theory NGB. On the basis of primitive recursion we consider \mu-recursive maps as partial pr maps. Special terminating general recursive maps considered are complexity controlled iterations. Map code evaluation is then given in terms of such an iteration. We discuss iterative pr map code evaluation versus termination conditioned soundness and based on this decidability of primitive recursive predicates.