4 Computational modal logic

Conditional Epistemic Planning

“…Add a new node m to T with M(m) = M(n) ⊗ E, and add an edge (n, m) with E(n, m) = E. The tree expansion rule is similar in structure to-and inspired by-the expansion rules used in tableau calculi, e.g. for modal and description logics [14]. Note that the expansion rule applies only to or-nodes, and that an applicable event model can only be used once at each node.…”

Terminating Tableau Systems for Hybrid Logic with Difference and Converse

“…We work with tableau-based decision methods since they may be realized with gracefully degrading performance even if the worst-case complexity of the decision problem is prohibitive. This is witnessed by the success of tableau-based decision procedures for description logics [2,16], which are modal logics adapted to knowledge representation.…”

“…Only for formulas with converse modalities we have to resort to the usual chain-based blocking scheme [22,17,16]. The patternbased control yields a smaller search space than chain-based blocking, and this shows in the performance of a first implementation.…”

Topics in Knowledge Bases: Epistemic Ontologies and Secrecy-preserving Reasoning

“…Let Σ = A, T be a knowledge base. We define the concept of a constraint graph by generalizing the idea of a completion tree in [53], and build it starting from a single node representing the constraint system obtained from A and an input query and repeatedly applying expansion rules. The constraints in constraint systems are of the form a :…”

“…Remark Firstly, note that Theorem 2.3.6 applies to general directed graphs (rather than just trees as, e.g., in [53] …”