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In this paper, we introduce a set representation called polynomial logical zonotopes for performing exact and computationally efficient reachability analysis on logical systems. We prove that through this polynomial-like construction, we…
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…
Rule-based models are attractive for various tasks because they inherently lead to interpretable and explainable decisions and can easily incorporate prior knowledge. However, such systems are difficult to apply to problems involving…
Automating the translation of natural language to first-order logic (FOL) is crucial for knowledge representation and formal methods, yet remains challenging. We present a systematic evaluation of fine-tuned LLMs for this task, comparing…
It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. Despite the vast…
We consider (logical) reasoning for regular expressions with lookahead (REwLA). In this paper, we give an axiomatic characterization for both the (match-)language equivalence and the largest substitution-closed equivalence that is sound for…
In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
Logic programming (LP) is a programming language based on first-order Horn clause logic that uses SLD-resolution as a semi-decision procedure. Finite SLD-computations are inductively sound and complete with respect to least Herbrand models…
Datalog-based languages are regaining popularity as a powerful abstraction for expressing recursive computations in domains such as program analysis and graph processing. However, existing systems often face a trade-off between efficiency…
We introduce \emph{TAPO-Structured Description Logic} (TAPO--DL), a formal extension of classical description logic designed to model \emph{information behavior} as a structured, dynamic process. TAPO--DL extends the standard T--Box/A--Box…
In systems verification we are often concerned with multiple, inter-dependent properties that a program must satisfy. To prove that a program satisfies a given property, the correctness of intermediate states of the program must be…
Constraint Logic Programming (CLP) and Hereditary Harrop formulas (HH) are two well known ways to enhance the expressivity of Horn clauses. In this paper, we present a novel combination of these two approaches. We show how to enrich the…
Similarity-based Logic Programming (briefly, SLP ) has been proposed to enhance the LP paradigm with a kind of approximate reasoning which supports flexible information retrieval applications. This approach uses a fuzzy similarity relation…
Dual Horn clauses mirror key properties of Horn clauses. This paper explores the ``other side of the looking glass'' to reveal some expected and unexpected symmetries and their practical uses. We revisit Dual Horn clauses as enablers of a…
Descriptive Complexity has been very successful in characterizing complexity classes of decision problems in terms of the properties definable in some logics. However, descriptive complexity for counting complexity classes, such as FP and…
Verification of properties of first order logic with two variables FO2 has been investigated in a number of contexts. Over arbitrary structures it is known to be decidable with NEXPTIME complexity, with finitely satisfiable formulas having…
A very desirable Datalog extension investigated by many researchers in the last thirty years consists in allowing the use of the basic SQL aggregates min, max, count and sum in recursive rules. In this paper, we propose a simple…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is…