The use of expressive logical axioms to specify derived predicates often allows planning domains to be formulated more compactly and naturally. We consider axioms in the form of a logic program with recursively defined predicates and negation-as-failure, as in PDDL 2.2. We show that problem formulations with axioms are not only more elegant, but can also be easier to solve, because specifying indirect action effects via axioms removes unnecessary choices from the search space of the planner. Despite their potential, however, axioms are not widely supported, particularly by cost-optimal planners. We draw on the connection between planning axioms and answer set programming to derive a consistency-based relaxation, from which we obtain axiom-aware versions of several admissible planning heuristics, such as hmax and pattern database heuristics.
During the last decade, it has been widely shown how modal logics provide suitable tools for various theoretical formalizations in computer science. In fact, many modal systems can be found in the literature, and there are a number of areas where such logics are used. Most popular readings of the modal formula a are, for example, "0 is necessarily frue" (standard modal logic), "a will always be true" (temporal logic), "X knows fhaf a" or "X believes that a" (epistemic logic), or "after executing some program a, a will be frue" (dynamic logic), etc. In general, only one fype of modality is considered, i.e.
SAT solvers have become efficient for solving NP-complete problems (and beyond). Usually, those problems are solved by direct translation to SAT or by solving iteratively SAT problems in a procedure like CEGAR. Recently, a new recursive CEGAR loop working with two abstraction levels, called RECAR, was proposed and instantiated for modal logic K. We aim to complete this work for modal logics based on axioms (B), (D), (T), (4) and (5. Experimental results show that the approach is competitive against state-of-the-art solvers for modal logics K, KT, and S4.
Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for a given functor, thus covering a wide range of reasoning principles including, e.g., probabilistic, graded, default, or coalitional operators. Specifically, we establish generic criteria for a given coalgebraic hybrid logic to admit named canonical models, with ensuing completeness proofs for pure extensions on the one hand, and for an extended hybrid language with local binding on the other. We instantiate our framework with a number of examples. Notably, we prove completeness of graded hybrid logic with local binding.