151 research outputs found
On the Semantics of Gringo
Input languages of answer set solvers are based on the mathematically simple
concept of a stable model. But many useful constructs available in these
languages, including local variables, conditional literals, and aggregates,
cannot be easily explained in terms of stable models in the sense of the
original definition of this concept and its straightforward generalizations.
Manuals written by designers of answer set solvers usually explain such
constructs using examples and informal comments that appeal to the user's
intuition, without references to any precise semantics. We propose to approach
the problem of defining the semantics of gringo programs by translating them
into the language of infinitary propositional formulas. This semantics allows
us to study equivalent transformations of gringo programs using natural
deduction in infinitary propositional logic.Comment: Proceedings of Answer Set Programming and Other Computing Paradigms
(ASPOCP 2013), 6th International Workshop, August 25, 2013, Istanbul, Turke
Measurable selection for purely atomic games
A general selection theorem is presented constructing a measurable mapping from a state space to a parameter space under the assumption that the state space can be decomposed as a collection of countable equivalence classes under a smooth equivalence relation. It is then shown how this selection theorem can be used as a general purpose tool for proving the existence of measurable equilibria in broad classes of several branches of games when an appropriate smoothness condition holds, including Bayesian games with atomic knowledge spaces, stochastic games with countable orbits, and graphical games of countable degree—examples of a subclass of games with uncountable state spaces that we term purely atomic games. Applications to repeated games with symmetric incomplete information and acceptable bets are also presented
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Mathematical Logic: Proof Theory, Constructive Mathematics (hybrid meeting)
The Workshop "Mathematical Logic: Proof Theory,
Constructive Mathematics" focused on
proofs both as formal derivations in deductive systems as well as on
the extraction of explicit computational content from
given proofs in core areas of ordinary mathematics using proof-theoretic
methods. The workshop contributed to the following research strands: interactions between foundations and applications; proof mining; constructivity in classical logic; modal logic and provability logic; proof theory and theoretical computer science; structural proof theory
Probability Logic for Harsanyi Type Spaces
Probability logic has contributed to significant developments in belief types
for game-theoretical economics. We present a new probability logic for Harsanyi
Type spaces, show its completeness, and prove both a de-nesting property and a
unique extension theorem. We then prove that multi-agent interactive
epistemology has greater complexity than its single-agent counterpart by
showing that if the probability indices of the belief language are restricted
to a finite set of rationals and there are finitely many propositional letters,
then the canonical space for probabilistic beliefs with one agent is finite
while the canonical one with at least two agents has the cardinality of the
continuum. Finally, we generalize the three notions of definability in
multimodal logics to logics of probabilistic belief and knowledge, namely
implicit definability, reducibility, and explicit definability. We find that
S5-knowledge can be implicitly defined by probabilistic belief but not reduced
to it and hence is not explicitly definable by probabilistic belief
Temporal Answer Set Programming
[Abstract]
Commonsense temporal reasoning is full of situations that require drawing default conclusions, since we rarely have all the information available. Unfortunately,
most modal temporal logics cannot accommodate default reasoning, since they typically deal with a monotonic inference relation. On the other hand, non-monotonic approaches are very expensive and their treatment of time is not so well delimited and studied as in modal logic.
Temporal Equilibrium Logic (TEL) is the first non-monotonic temporal logic
which fully covers the syntax of some standard modal temporal approach
without requiring further constructions. TEL shares the syntax of Linear-time
Temporal Logic (LTL) (first proposed by Arthur Prior and later extended by
Hans Kamp) which has become one of the simplest, most used and best known
temporal logics in Theoretical Computer Science.
Although TEL had been already defined, few results were known about its fundamental properties and nothing at all on potential computational methods that could be applied for practical purposes. This situation unfavourably contrasted with the huge body of knowledge available for LTL, both in well-known formal properties and in computing methods with practical implementations.
In this thesis we have mostly filled this gap, following a research program that
has systematically analysed different essential properties of TEL and, simultaneously, built computational tools for its practical application. As an overall, this thesis collects a corpus of results that constitutes a significant breakthrough in the knowledge about TEL.[Resumen]
El razonamiento temporal del sentido común está lleno de situaciones que requieren suponer conclusiones por defecto, puesto que raramente contamos con toda la información disponible. Lamentablemente, la mayoría de lógicas modales temporales no permiten modelar este tipo de razonamiento por defecto
debido a que, típicamente, se definen por medio de relaciones de inferencia
monótonas. Por el contrario, las aproximaciones no monótonas existentes son
típicamente muy costosas pero su manejo del tiempo no está tan bien delimitado como en lógica modal.
Temporal Equilibrium Logic (TEL) es la primera lógica temporal no monótona
que cubre totalmente la sintaxis de alguna de las lógicas modales tradicionales
sin requerir el uso de más construcciones. TEL comparte la sintaxis de Linear-time Temporal Logic (LTL) (formalismo propuesto por Arthur Prior y posteriormente extendido por Hans Kamp), que es una de las lógicas más
simples, utilizadas y mejor conocidas en Teoría de la Computación.
Aunque TEL había sido definido, muy pocas propiedades eran conocidas,
lo que contrastaba con el vasto conocimiento de LTL que está presente en el estado del arte. En esta tesis hemos estudiado diferentes aspectos de TEL, una novedosa combinación de lógica modal temporal y un formalismo no monótono.
A grandes rasgos, esta tesis recoge un conjunto de resultados, tanto desde el punto de vista teórico como práctico, que constituye un gran avance en lo relativo al conocimiento sobre TEL.[Resumo]
O razoamento do sentido común aplicado ao caso temporal está cheo de situacións
que requiren supoñer conclusións por defecto, posto que raramente
contamos con toda a información dispoñible. Lamentablemente a maioría de
lóxicas modais temporáis non permiten modelar este tipo de razoamento por
defecto debido a que, típicamente, están definidas por medio de relacións de
inferencia monótonas. Pola contra, as aproximacións non monótonas existentes
son moi costosos e o seu tratamento do tempo non está ben tan delimitado
nin estudiado como nas lóxicas modais.
Temporal Equilibrium Logic (TEL) é a primeira aproximación non monótona
que cubre totalmente a sintaxe dalgunha das lóxicas modais traidicionáis
sen requerir o uso de máis construccións. TEL comparte a sintaxe de Lineartime
Temporal Logic (LTL) (formalismo proposto por Arthur Prior e extendido
posteriormente por Hans Kamp), que é considerada unha das lóxicas modais
máis simples, utilizadas e coñecidas dentro da Teoría da Computación.
Aínda que TEL xa fora definido previamente, moi poucas das súas propiedades
eran coñecidas, dato que contrasta co vasto coñecemento de LTL existente
no estado da arte. Nesta tese, estudiamos diferentes aspectos de TEL,
unha novidosa combinación de lóxica modal temporal e un formalimo non
monótono. A grandes rasgos, esta tese recolle un conxunto de resultados, tanto
dende o punto de vista teórico como práctico, que constitúe un gran avance
no relativo ó coñecemento sobre o formalismo TEL
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