Conservative Retractions of Propositional Logic Theories by Means of Boolean Derivatives: Theoretical Foundations

Abstract

Abstract. We present a specialised (polynomial-based) rule for the propositional logic called the Independence Rule, which is useful to compute the conservative retractions of propositional logic theories. In this paper we show the soundness and completeness of the logical calculus based on this rule, as well as other applications. The rule is defined by means of a new kind of operator on propositional formulae. It is based on the boolean derivatives on the polynomial ring F2 [x].

Confidence-Based Reasoning with Local Temporal Formal Contexts

“…However, the summation of additional data and attributes could make it necessary to apply conservative retraction methods [5,2] to work with a contextual KB of a feasible size.…”

Bounded Rationality for Data Reasoning Based on Formal Concept Analysis

“…Two options have been considered for solving this problem by FCA. The first one is based on avoiding inconsistencies using conservative retraction [13]. The aim is to remove one attribute from incompatible pairs in contextual KB, next to present related attribute proof.…”

A logic-algebraic tool for reasoning with Knowledge-Based Systems

“…Then the entailment problem with respect to K is considered. For this strategy to be successful -valid and complete-K must be a conservative extension of K (or, equivalently, K a conservative retraction of K [10]). A knowledge base K in the language L is a conservative retraction of K if K is an extension of K such that every L -fórmula entailed by K is also entailed by K .…”

“…Taking into account the aforementioned motivations, the aim of this paper is twofold. First, we intend to present a complete and detailed exposition of the foundations of the independence rule (That can be considered a tool for variable forgetting), whose basic ideas were published in [10], since no detailed exposition has been published until now. In fact, we generalize the cited paper by stating the results for any operator that induces a conservative retraction, leading as consequence that our case, the independence rule, is useful to compute the retractions.…”