Related papers: Generalized Complexity of ALC Subsumption
Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for…
Clustering attempts to partition data instances into several distinctive groups, while the similarities among data belonging to the common partition can be principally reserved. Furthermore, incomplete data frequently occurs in many…
We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula…
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment to contexts involving relations of arity greater than two. Quantifiers in this logic are used 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,…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
We first show that infinite satisfiability can be reduced to finite satisfiability for all prenex formulas of Separation Logic with $k\geq1$ selector fields ($\seplogk{k}$). Second, we show that this entails the decidability of the finite…
Decomposing hard problems into subproblems often makes them easier and more efficient to solve. With large language models (LLMs) crossing critical reliability thresholds for a growing slate of capabilities, there is an increasing effort to…
We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…
In the context of ontology-mediated querying with description logics (DLs), we study the data complexity of queries in which selected predicates can be closed (OMQCs). We provide a non-uniform analysis, aiming at a classification of the…
Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopological space. Such spaces satisfying all the axioms of GLP are…
In this paper we study the expressive power of Horn-formulae in dependence logic and show that they can express NP-complete problems. Therefore we define an even smaller fragment D-Horn* and show that over finite successor structures it…
Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough…
Uniform one-dimensional fragment UF1^= is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified…
We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…
Optimization - minimization or maximization - in the lattice of subsets is a frequent operation in Artificial Intelligence tasks. Examples are subset-minimal model-based diagnosis, nonmonotonic reasoning by means of circumscription, or…
In this work we investigate the computational complexity of the satisfiability problem of sub-fragments of the Bernays-Schoenfinkel class of first-order logic, also known as EPR (Effectively Propositional). While Bernays-Schoenfinkel is…
We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our main result is a strategy to approximately recover the unknown dictionary…