Abductive reasoning in normal residuated logic programming via bipolar max-product fuzzy relation equations

Abstract

Fuzzy relation equations have recently been extended to a more general framework in which the unknown variables appear together with their logical negation connectives, giving rise to the called bipolar fuzzy relation equations. This paper shows an abductive procedure for a special kind of normal residuated logic program by means of bipolar maxproduct fuzzy relation equations. From this procedure, interesting properties relating the models of a given normal residuated logic program to the solutions of its corresponding bipolar max-product fuzzy relation equation is deduced.

On the impact of sup‐compositions in the resolution of multi‐adjoint relation equations

“…An abduction problem is the process of looking for possible antecedents when consequents and weights are known. This process in a MALP is equivalent to a MARE [11]. Because of this connection between MALP and MARE, the possible antecedents of a situation are described by the solution set of a MARE.…”

“…Additionally, the logic program that leads to the abduction process will have the same requirements as the one presented in Lobo et al [11], that is: There are no cyclic dependencies in the rules of the program. Bodies of the rules can only contain one propositional symbol. For the sake of simplicity, we will assign the same residuated implication to all rules with the same body. …”

“…Additionally, the logic program that leads to the abduction process will have the same requirements as the one presented in Lobo et al [11], that is:…”

“…Its relevance has motivated a deep research on resolution techniques [6][7][8][9]. Simultaneously, a large number of applications for FRE have arisen in multiple fields such as logic programming [10], abductive reasoning [11], optimization [12], medical diagnosis [13], and bipolar information [14][15][16].…”

Bipolar equations on complete distributive symmetric residuated lattices: The case of a join-irreducible right-hand side

“…Within this context of bipolarity, bipolar fuzzy relational equations were introduced in [20] as a generalization of fuzzy relational equations [30,31] (one of the core research topics in fuzzy set theory [15,18]), where the unknown variables and their negations appear simultaneously. Most, if not all, publications on bipolar fuzzy relational equations are restricted to the real unit interval [20,26,27,33], as was the case for fuzzy relational equations in the early days. Moreover, the equations considered in the literature are all of the type max- * , with * a triangular norm (t-norm, for short).…”