We introduce metric temporal description logics (mTDLs) as combinations of the classical description logic ALC with (a) LTL, an extension of the temporal logic LTL with succinctly represented intervals, and (b) metric temporal logic MTL, extending LTL with capabilities to quantitatively reason about time delays. Our main contributions are algorithms and tight complexity bounds for the satisfiab...

The semantics of logic programs is commonly deened as the least xed point of an appropriate meaning operator. In case of normal programs, however, some undesired results do occur and it has recently been suggested to apply metric methods in order to overcome these problems. We show in this paper that these metric methods can be directly implemented by recurrent connectionist networks giving ris...

In this paper we study the intermediate logic MLO(X ) of open subsets of a metric space X . This logic is closely related to Medvedev’s logic of finite problemsML. We prove several facts about this logic: its inclusion in ML, impossibility of its finite axiomatization and indistinguishability from ML within some large class of propositional formulas.

Probabilistic inference can be realized using weighted model counting. Despite a lot of progress, computing weighted model counts exactly is still infeasible for many problems of interest, and one typically has to resort to approximation methods. We contribute a new bounded approximation method for weighted model counting based on probabilistic logic programming principles. Our bounded approxim...

We present WECTL∗KD, a weighted branching time temporal logic to specify knowledge, and correct functioning behaviour in multi-agent systems (MAS). We interpret the formulae of the logic over models generated by weighted deontic interpreted systems (WDIS). Furthermore, we investigate a SAT-based bounded model checking (BMC) technique for WDIS and for WECTL∗KD.

We study the model-checking problem for weighted timed automata and the weighted CTL logic by the bisimulation approach. Weighted timed automata are timed automata extended with costs on both edges and locations. When the costs act as stopwatches, we get stopwatch automata with the restriction that the stopwatches cannot be reset and tested. The weighted CTL logic is an extension of TCTL that a...

Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. Several classical probabilistic inference tasks (such as MAP and computing marginals) have not yet received a lot of attention for this formalism. The contribution of this paper is that we develop efficient inference algorithms for these tasks. This is based on a conversion of the probab...

Extracting spatial-temporal knowledge from data is useful in many applications. It important that the obtained human-interpretable and amenable to formal analysis. In this letter, we propose a method trains neural networks learn properties form of weighted graph-based signal temporal logic (w-G...

We consider different types of aggregation operators such as the heavy ordered weighted averaging (HOWA) operator and the fuzzy ordered weighted averaging (FOWA) operator. We introduce a new extension of the OWA operator called the fuzzy heavy ordered weighted averaging (FHOWA) operator. The main characteristic of this aggregation operator is that it deals with uncertain information represented...