Multimodal logic programming using equational and order-sorted logic

AbstractIn our previous works a method for automated theorem proving in modal logic, based on algebraic and equational techniques, was proposed. In this paper we extend the method to multimodal logic and apply it to modal logic programming. Multimodal systems under consideration have a finite number of pairs of modal operators (♢i, □i) of any type among KD, KT, KD4, KT4, KF, and interaction axioms of the form □iA → □jA. We define a translation from such logical systems to specially tailored equational theories of classical order-sorted logic, preserving satisfiability, and then use SLD E-resolution for theorem proving in these theories

Parameter Structures for Parametrized Modal Operators

The parameters of the parameterized modal operators [p] and <p> usually represent agents (in the epistemic interpretation) or actions (in the dynamic logic interpretation) or the like. In this paper the application of the idea of parametrized modal operators is extended in in two ways: First of all a modified neighbourhood semantics is defined which permits among others the interpretation of the parameters as probability values. A formula [.5] F may for example express the fact that in at least 50 % of all cases (worlds) F holds. These probability values can be numbers, qualitative descriptions and even arbitrary terms. Secondly a general theory of the parameters and in particular of the characteristic operations on the parameters is developed which unifies for example the multiplication of numbers in the probabilistic interpretation of the parameters and the sequencing of actions in the dynamic logic interpretation