An Algebra of Causal Chains
Pedro Cabalar, Jorge Fandinno

TL;DR
This paper introduces an algebraic framework for causal logic programs that associates justifications with true atoms, enabling analysis of causes, redundancies, and relevance through algebraic and lattice-based methods.
Contribution
It presents a novel algebra of truth values for causal logic programs, linking proof trees to algebraic semantics and defining causal stable models.
Findings
Established a one-to-one correspondence between proof trees and algebraic interpretations.
Defined an algebra with addition, product, and concatenation operations for justifications.
Proved properties of the semantics, including fixpoint computation and causal stable models.
Abstract
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main contribution of this paper is that we capture justifications into an algebra of truth values with three internal operations: an addition '+' representing alternative justifications for a formula, a commutative product '*' representing joint interaction of causes and a non-commutative product '.' acting as a concatenation or proof constructor. Using this multi-valued semantics, we obtain a one-to-one correspondence between the syntactic proof tree of a standard (non-causal) logic program and the interpretation of each true atom in a model. Furthermore, thanks to this algebraic characterization we can detect semantic properties like redundancy and relevance of…
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Logic, programming, and type systems · Advanced Algebra and Logic
