Numerical Analysis of Possibilistic Answer Set
Asraful Islam · 2021 IEEE Symposium Series on Computational Intelligence (SSCI) · 2021
Possibilistic logic program (PLP) is a logic system for representing incomplete and uncertain knowledge in a non-probabilistic way. One of the existing semantics is less expressive and the other one is not tools-oriented, none of them characterises the possibilistic integrity constraints, resulting in the semantics are not compatible for software development. In this paper, we consider a monotonic PLP-a fully grounded possibilistic definite logic program (PDLP)-and formalise a tools-oriented numerical method to determine the answer set of the PDLP. To do so, firstly, we define an atom-wise transformation of a PDLP into a system of equality constraints of necessity degrees. Secondly, we formalise iterative formulas to determine those necessity degrees. Finally, we extend our method to characterise the possibilistic integrity constraints appearing in PDLP. We consider the theoretical aspect to understand the efficiency and the computational complexity of the proposed method and prove that the number of iterations required here for a PDLP is at best the number of rules of the program.