Dependence in Propositional Logic: Formula-Formula Dependence and Formula Forgetting -- Application to Belief Update and Conservative Extension

Dependence is an important concept for many tasks in artificial intelligence. A task can be executed more efficiently by discarding something independent from the task. In this paper, we propose two novel notions of dependence in propositional logic: formula-formula dependence and formula forgetting. The first is a relation between formulas capturing whether a formula depends on another one, while the second is an operation that returns the strongest consequence independent of a formula. We also apply these two notions in two well-known issues: belief update and conservative extension. Firstly, we define a new update operator based on formula-formula dependence. Furthermore, we reduce conservative extension to formula forgetting.Comment: We find a mistake in this version and we need a period of time to fix i

Prime Forms in Possibilistic Logic

Possibilistic logic is a weighted logic used to represent uncertain and inconsistent knowledge. Its semantics is often defined by a possibility distribution, which is a function from a set of interpretations to a totally ordered scale. In this paper, we consider a new semantic characteristics of knowledge bases in possibilistic logic (or possibilistic knowledge bases) by a generalized notion of propositional prime implicant, which we call prioritized prime implicant. We first consider several desirable properties of a prioritized prime implicant for characterizing possibilistic knowledge bases. Some examples show that existing generalizations of prime implicant in possibilistic logic do not satisfy all of these properties. We then provide a novel definition of prioritized prime implicant, which is a set of weighted literals that may be inconsistent. We show that the prioritized prime implicants satisfy all the desirable properties. Finally, we discuss the problem of computing prioritized prime implicants of a possibilistic knowledge base

The Incremental Satisfiability Problem for a Two Conjunctive Normal Form

We propose a novel method to review K ⊢ φ when K and φ are both in Conjunctive Normal Forms (CF). We extend our method to solve the incremental satisfiablity problem (ISAT), and we present different cases where ISAT can be solved in polynomial time. Especially, we present an algorithm for 2-ISAT. Our last algorithm allow us to establish an upper bound for the time-complexity of 2-ISAT, as well as to establish some tractable cases for the 2-ISAT problem

Diseño de un algoritmo para la revisión de creencias entre formas conjuntivas

"El problema a tratar en este trabajo de tesis es proponer un algoritmo para la revisión y actualización de una base de conocimiento usando lógica proposicional. Una base de conocimiento almacena conocimiento en una forma legible para la computadora, usualmente con el fin de obtener razonamiento deductivo automático aplicado a ellas, las cuales contienen una serie de datos en forma de reglas que describen el conocimiento de manera lógicamente consistente usando operadores lógicos"