Related papers: The Complexity of Poor Man's Logic
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…
Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…
A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames have already been established. By "traditional" classes of frames, we mean those…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL)…
Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for solving NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at…
A relation modification problem gets a logical structure and a natural number k as input and asks whether k modifications of the structure suffice to make it satisfy a predefined property. We provide a complete classification of the…
This paper studies the complexity of determining whether a formula in the modal logics characterizing the nested-simulation semantics is characteristic for some process, which is equivalent to determining whether the formula is satisfiable…
We study the satisfiability problem for a modal logic expressing knowing-how assertions, which captures an agent's ability to achieve a given goal under the standard semantics based on linear plans. Our main result shows that satisfiability…
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…
Standard epistemic logic studies propositional knowledge, yet many other types of knowledge such as "knowing whether", "knowing what", "knowing how" are frequently and widely used in everyday life as well as academic fields. In…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
Let L be some extension of classical propositional logic. The non-iterated probabilistic logic over L, is the logic PL that is defined by adding non-nested probabilistic operators in the language of L. For example in PL we can express a…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even…
We consider logic-based argumentation in which an argument is a pair (Fi,al), where the support Fi is a minimal consistent set of formulae taken from a given knowledge base (usually denoted by De) that entails the claim al (a formula). We…
This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…
Probabilistic justification logic is a modal logic with two kind of modalities: probability measures and explicit justification terms. We present a tableau procedure that can be used to decide the satisfiability problem for this logic in…
Many natural optimization problems derived from $\sf NP$ admit bilevel and multilevel extensions in which decisions are made sequentially by multiple players with conflicting objectives, as in interdiction, adversarial selection, and…