Artículos con la etiqueta ‘Lógica’

A Note on the Fixed Points in Justification Logics

Por • 26 mar, 2014 • Category: Educacion

In this note we study the effect of adding fixed points to justification logics. We introduce two extensions of justification logics: extensions by fixed point (or diagonal) operators, and extensions by least fixed points. The former is a justification version of Smory\`{n}ski’s Diagonalization Operator Logic, and the latter is a justification version of Kozen’s modal μ -calculus. We also introduce fixed point extensions of Fitting’s quantified logic of proofs, and formalize the Knower Paradox and the Surprise Test Paradox in these extensions. By interpreting a surprise statement as a statement for which there is no justification, we give a solution to the self-reference version of the Surprise Test Paradox in quantified logic of proofs.



La diferencia entre lógicas y el cambio de significado de las conectivas: un enfoque categorista

Por • 24 mar, 2014 • Category: Opinion

En este artículo tratamos de hacer plausible la hipótesis de que las conectivas de diferentes lógicas no necesariamente difieren en significado. Utilizando el tratamiento categorista de las conectivas, argumentaremos contra la tesis quineana de que la diferencia de lógicas implica diferencia de significado entre sus conectivas, y ubicamos el cambio de tema en la diferencia de objetos más bien que en una tal diferencia de significado. Finalmente, intentamos mostrar que ese tratamiento categorista es una forma de minimalismo semántico, de acuerdo con el cual no todos los elementos semánticos usuales son relevantes para determinar el significado de las conectivas.



On Strongly First-Order Dependencies

Por • 19 mar, 2014 • Category: Ciencia y tecnología

We prove that the expressive power of first-order logic with team semantics plus contradictory negation does not rise beyond that of first-order logic (with respect to sentences), and that the totality atoms of arity k +1 are not definable in terms of the totality atoms of arity k. We furthermore prove that all first-order nullary and unary dependencies are strongly first order, in the sense that they do not increase the expressive power of first order logic if added to it.



Verdad, creencia y convención en el poema de Parménides

Por • 17 mar, 2014 • Category: Opinion

Esta intervención trata de resumir las líneas generales de una nueva interpretación del conjunto de los fragmentos de Parménides, tomando pie de la relación entre forma poética y razonamiento lógico (I). Se sostiene, en particular, que el ‘ES’ de la diosa ha de entenderse en el sentido de una predicación de verdad necesaria, cuya negación (‘NO ES’) resulta contradictoria consigo misma (II), por lo cual ‘lo-que-ES’ ha de ser lo que es de modo eterno, perfecto e inmutable, mientras que las cosas de la realidad ordinaria no pueden ser lo que se supone que son más que “de nombre” (III); que el problema de la mal llamada dóxa sólo se resuelve con tal de distinguir la teoría física del poema –cuyo principio es la mezcla y unidad de los opuestos– de las engañosas creencias de los mortales en la rígida separación (lógica y física) de los términos opuestos (IV)…



Restructuring Logic

Por • 12 mar, 2014 • Category: Filosofía

The outline of a programme for restructuring mathematical logic. We explain what we mean by “restructuring” and carry out exemplary parts of the programme



Topos Semantics for Higher-Order Modal Logic

Por • 6 mar, 2014 • Category: Educacion

We define the notion of a model of higher-order modal logic in an arbitrary elementary topos E . In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the subobject classifier ΩE , but rather by a suitable complete Heyting algebra H . The canonical map relating H and ΩE both serves to interpret equality and provides a modal operator on H in the form of a comonad. Examples of such structures arise from surjective geometric morphisms f:F→E , where H=f∗ΩF . The logic differs from non-modal higher-order logic in that the principles of functional and propositional extensionality are no longer valid but may be replaced by modalized versions. The usual Kripke, neighborhood, and sheaf semantics for propositional and first-order modal logic are subsumed by this notion.



Trends in Computer Network Modeling Towards the Future Internet

Por • 6 mar, 2014 • Category: Ciencia y tecnología

This article provides a taxonomy of current and past network modeling efforts. In all these efforts over the last few years we see a trend towards not only describing the network, but connected devices as well. This is especially current given the many Future Internet projects, which are combining different models, and resources in order to provide complete virtual infrastructures to users. An important mechanism for managing complexity is the creation of an abstract model, a step which has been undertaken in computer networks too. The fact that more and more devices are network capable, coupled with increasing popularity of the Internet, has made computer networks an important focus area for modeling. The large number of connected devices creates an increasing complexity which must be harnessed to keep the networks functioning.



Creature forcing and five cardinal characteristics of the continuum

Por • 13 feb, 2014 • Category: Opinion

We use a (countable support) creature construction to show that consistently
d=ℵ 1 =cov(NULL)



Scheme representation for first-order logic

Por • 13 feb, 2014 • Category: Educacion

Although contemporary model theory has been called “algebraic geometry minus fields”, the formal methods of the two fields are radically different. This dissertation aims to shrink that gap by presenting a theory of logical schemes, geometric entities which relate to first-order logical theories in much the same way that algebraic schemes relate to commutative rings. The construction relies on a Grothendieck-style representation theorem which associates every coherent or classical first-order theory with an affine scheme: a topological groupoid (the spectrum of the theory) together with a sheaf of (local) syntactic categories.



Generalizations of the Kolmogorov-Barzdin embedding estimates

Por • 11 feb, 2014 • Category: Ciencia y tecnología

We consider several ways to measure the `geometric complexity’ of an embedding from a simplicial complex into Euclidean space. One of these is a version of `thickness’, based on a paper of Kolmogorov and Barzdin. We prove inequalities relating the thickness and the number of simplices in the simplicial complex, generalizing an estimate that Kolmogorov and Barzdin proved for graphs. We also consider the distortion of knots. We give an alternate proof of a theorem of Pardon that there are isotopy classes of knots requiring arbitrarily large distortion. This proof is based on the expander-like properties of arithmetic hyperbolic manifolds.