FO(FD): Extending classical logic with rule-based fixpoint definitions

Abstract

We introduce fixpoint definitions, a rule-based reformulation of fixpoint constructs. The logic FO(FD), an extension of classical logic with fixpoint definitions, is defined. We illustrate the relation between FO(FD) and FO(ID), which is developed as an integration of two knowledge representation paradigms. The satisfiability problem for FO(FD) is investigated by first reducing FO(FD) to difference logic and then using solvers for difference logic. These reductions are evaluated in the computation of models for FO(FD) theories representing fairness conditions and we provide potential applications of FO(FD).

Recursive Rules with Aggregation: A Simple Unified Semantics

“…The study of recursive rules with negation goes back at least to Russell's paradox, discovered over 120 years ago [35]. Many logic languages and disagreeing semantics have since been proposed, with significant complications and challenges described in various survey and overview articles, e.g., [8,23,52,61], and in works on relating and unifying different semantics, e.g., [10,17,18,34,37,42,51,55].…”

Improving Parity Game Solvers with Justifications

“…The first contribution of this paper is to propose an algorithm that maintains an improved datastructure called a justification graph, to store a single (partial) winning strategy during execution. Justification graphs as we use it here, were first introduced in Hou et al [11] in the context of a semantic study of nested least and greatest fixpoint definitions.…”

“…A parity game solver determines for each node the winner and a winning strategy. Many problems over boolean equation systems [5,13], µ-calculus [10,20], nested fixpoints [11] and temporal logics such as LTL, CTL and CTL* [10] reduce to parity games.…”

Conceptual Representations for Computational Concept Creation

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