Forgetting complex propositions

This paper uses possible-world semantics to model the changes that may occur in an agent's knowledge as she loses information. This builds on previous work in which the agent may forget the truth-value of an atomic proposition, to a more general case where she may forget the truth-value of a propositional formula. The generalization poses some challenges, since in order to forget whether a complex proposition $\pi$ is the case, the agent must also lose information about the propositional atoms that appear in it, and there is no unambiguous way to go about this. We resolve this situation by considering expressions of the form $[\boldsymbol{\ddagger} \pi]\varphi$, which quantify over all possible (but minimal) ways of forgetting whether $\pi$. Propositional atoms are modified non-deterministically, although uniformly, in all possible worlds. We then represent this within action model logic in order to give a sound and complete axiomatization for a logic with knowledge and forgetting. Finally, some variants are discussed, such as when an agent forgets $\pi$ (rather than forgets whether $\pi$) and when the modification of atomic facts is done non-uniformly throughout the model

Deducción y generación de modelos de cardinalidad finita

Presentamos un procedimiento de tablas semánticas distinto de las estándar en el tratamiento dado a las sentencias de la clase δ, proponiendo modificaciones de esta regla que eviten la generación de ramas infinitas. Las nuevas tablas se revelan útiles para el estudio de lenguajes lógico-formales con semántica finitaria, en particular como procedimiento para definir modelos finitos de sentencias satisfacibles. Mostramos también la aplicabilidad de estos resultados al análisis de la ambigüedad y otros fenómenos en la interpretación del discurso

Dynamic consequence and public announcement

Junta de Andalucía P08-HUM- 04159European Research Council EPS 313360