Related papers: Complexity of the interpretability logic IL

Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…

We consider the satisfiability problem for the two-variable fragment of first-order logic over finite unranked trees. We work with signatures consisting of some unary predicates and the binary navigational predicates child, right sibling,…

Reachability for piecewise affine systems is known to be undecidable, starting from dimension $2$. In this paper we investigate the exact complexity of several decidable variants of reachability and control questions for piecewise affine…

We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. Assuming P != PSPACE, the existence or nonexistence of such efficient…

We investigate the complexity of satisfiability for finite-variable fragments of propositional dynamic logics. We consider three formalisms belonging to three representative complexity classes, broadly understood,---regular PDL, which is…

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…

The earlier paper "Introduction to clarithmetic I" constructed an axiomatic system of arithmetic based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proved its soundness and extensional completeness with respect…

There are a number of results saying that for certain "path-following" algorithms that solve PPAD-complete problems, the solution obtained by the algorithm is PSPACE-complete to compute. We conjecture that these results are special cases of…

The class of local languages is a well-known subclass of the regular languages that admits many equivalent characterizations. In this short note we establish the PSPACE-completeness of the problem of determining, given as input a…

We consider the one-variable fragment of first-order logic extended with Presburger constraints. The logic is designed in such a way that it subsumes the previously-known fragments extended with counting, modulo counting or cardinality…

We conceptualize explainability in terms of logic and formula size, giving a number of related definitions of explainability in a very general setting. Our main interest is the so-called special explanation problem which aims to explain the…

We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…

It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…

The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…

We show that it is coNP-complete to decide whether a given proof structure of pomset logic is a correct proof net, using the graph-theoretic used in a previous paper of ours (arXiv:1901.10247).

Feature attribution methods are popular for explaining neural network predictions, and they are often evaluated on metrics such as comprehensiveness and sufficiency. In this paper, we highlight an intriguing property of these metrics: their…

We investigate the satisfiability and finite satisfiability problem for probabilistic computation-tree logic (PCTL) where operators are not restricted by any step bounds. We establish decidability for several fragments containing…

How to handle division in systems that compute with logical formulas involving what would otherwise be polynomial constraints over the real numbers is a surprisingly difficult question. This paper argues that existing approaches from both…

We study the logic FO(~), the extension of first-order logic with team semantics by unrestricted Boolean negation. It was recently shown axiomatizable, but otherwise has not yet received much attention in questions of computational…

It is known that the existential theory of equations in free groups is decidable. This is a famous result of Makanin. On the other hand it has been shown that the scheme of his algorithm is not primitive recursive. In this paper we present…