Related papers: Generalized Satisfiability for the Description Log…
Weighted knowledge bases for description logics with typicality under a "concept-wise" multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to…
Strategy Logic (SL, for short) has been introduced by Mogavero, Murano, and Vardi as a useful formalism for reasoning explicitly about strategies, as first-order objects, in multi-agent concurrent games. This logic turns out to be very…
Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is…
It was shown in Alur et al. [1] that the problem of verifying finite concurrent systems through Linearizability is in EXPSPACE. However, there was still a complexity gap between the easy to obtain PSPACE lower bound and the EXPSPACE upper…
We analyze the computational complexity of admissibility and unifiability with parameters in transitive modal logics. The class of cluster-extensible (clx) logics was introduced in the first part of this series of papers. We completely…
The Description Logic EL has recently drawn considerable attention since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies.…
We determine the complexity of second-order HyperLTL satisfiability, finite-state satisfiability, and model-checking: All three are equivalent to truth in third-order arithmetic. We also consider two fragments of second-order HyperLTL that…
We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general orderings (instead of level mappings), like it is done in transformational approaches to logic program…
In logic-based knowledge representation, query answering has essentially replaced mere satisfiability checking as the inferencing problem of primary interest. For knowledge bases in the basic description logic ALC, the computational…
We prove that the problem of determining whether a finite logical matrix determines an algebraizable logic is complete for EXPTIME. The same result holds for the classes of order algebraizable, weakly algebraizable, equivalential and…
Modal logics are widely used in multi-agent systems to reason about actions, abilities, norms, or epistemic states. Combined with description logic languages, they are also a powerful tool to formalise modal aspects of ontology-based…
Epistemic logic programs (ELPs) are a popular generalization of standard Answer Set Programming (ASP) providing means for reasoning over answer sets within the language. This richer formalism comes at the price of higher computational…
Prior work has combined chain-of-thought prompting in large language models (LLMs) with programmatic representations to perform effective and transparent reasoning. While such an approach works well for tasks that only require forward…
Temporal Equilibrium Logic (TEL) is a promising framework that extends the knowledge representation and reasoning capabilities of Answer Set Programming with temporal operators in the style of LTL. To our knowledge it is the first…
These notes contain, among others, a proof that the average running time of an easy solution to the satisfiability problem for propositional calculus is, under some reasonable assumptions, linear (with constant 2) in the size of the input.…
We study the computational complexity of model checking and satisfiability problems of polyadic modal logics extended with permutations and Boolean operators on accessibility relations. First, we show that the combined complexity of the…
The Logic of Proofs, LP, and its successor, Justification Logic, is a refinement of the modal logic approach to epistemology in which proofs/justifications are taken into account. In 2000 Kuznets showed that satisfiability for LP is in the…
Standpoint linear temporal logic ($SLTL$) is a recently introduced extension of classical linear temporal logic ($LTL$) with standpoint modalities. Intuitively, these modalities allow to express that, from agent $a$'s standpoint, it is…
We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…
We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence, inclusion, and team logic. Our main result shows that the satisfiability and validity problems for…