Related papers: Solving unification in the description logic $\mat…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
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…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
We propose a novel algorithm for solving the composite Federated Learning (FL) problem. This algorithm manages non-smooth regularization by strategically decoupling the proximal operator and communication, and addresses client drift without…
For fragments L of first-order logic (FO) with counting quantifiers, we consider the definability problem, which asks whether a given L-formula can be equivalently expressed by a formula in some fragment of L without counting, and the more…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
The graph programming language GP 2 allows to apply sets of rule schemata (or "attributed" rules) non-deterministically. To analyse conflicts of programs statically, graphs labelled with expressions are overlayed to construct critical pairs…
The reasoning capabilities of large language models (LLMs) have been significantly improved through reinforcement learning (RL). Nevertheless, LLMs still struggle to consistently verify their own reasoning traces. This raises the research…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
A left-corner parsing algorithm with top-down filtering has been reported to show very efficient performance for unification-based systems. However, due to the nontermination of parsing with left-recursive grammars, top-down constraints…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
Federated learning (FL) is a recently proposed distributed machine learning paradigm dealing with distributed and private data sets. Based on the data partition pattern, FL is often categorized into horizontal, vertical, and hybrid…
We propose an analysis of corrections which models some of the requirements corrections place on context. We then show that this analysis naturally extends to the interaction of corrections with pronominal anaphora on the one hand, and…
We present a sound and complete unification procedure for deterministic higher-order patterns, a class of simply-typed lambda terms introduced by Yokoyama et al. which comes with a deterministic matching problem. Our unification procedure…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
Federated Learning (FL) has been becoming a popular interdisciplinary research area in both applied mathematics and information sciences. Mathematically, FL aims to collaboratively optimize aggregate objective functions over distributed…
We present new algorithm for computing the union and intersection of all justifications for a given ontological consequence without first computing the set of all justifications. Through an empirical evaluation, we show that our approach…
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…