相关论文: Light Logics and Optimal Reduction: Completeness a…

We present in this paper a reformulation of the usual set-theoretical semantics of the description logic $\mathcal{ALC}$ with general TBoxes by using categorical language. In this setting, $\mathcal{ALC}$ concepts are represented as…

We generalise the termination method of higher-order polynomial interpretations to a setting with impredicative polymorphism. Instead of using weakly monotonic functionals, we interpret terms in a suitable extension of System F-omega. This…

We introduce LAMPO, a novel paradigm that leverages Large Language Models (LLMs) for solving few-shot multi-class ordinal classification tasks. Unlike conventional methods, which concatenate all demonstration examples with the test instance…

The \it{Ambient Logic} (AL) has been proposed for expressing properties of process mobility in the calculus of Mobile Ambients (MA), and as a basis for query languages on semistructured data. We study some basic questions concerning the…

Since the seminal work of J. A. Robinson on resolution, many lifting lemmas for simplifying proofs of completeness of resolution have been proposed in the literature. In the logic programming framework, they may also help to detect some…

Logic-based abduction finds important applications in artificial intelligence and related areas. One application example is in finding explanations for observed phenomena. Propositional abduction is a restriction of abduction to the…

The dependently-typed lambda calculus LF is often used as a vehicle for formalizing rule-based descriptions of object systems. Proving properties of object systems encoded in this fashion requires reasoning about formulas over LF typing…

Extending the popular Answer Set Programming (ASP) paradigm by introspective reasoning capacities has received increasing interest within the last years. Particular attention is given to the formalism of epistemic logic programs (ELPs)…

We design a library for binary field arithmetic and we supply a core API which is completely developed in DLAL, extended with a fix point formula. Since DLAL is a restriction of linear logic where only functional programs with polynomial…

We prove two completeness results for Kleene algebra with tests and a top element, with respect to guarded string languages and binary relations. While the equational theories of those two classes of models coincide over the signature of…

This paper presents LITE, an LLM-based evaluation method designed for efficient and flexible assessment of taxonomy quality. To address challenges in large-scale taxonomy evaluation, such as efficiency, fairness, and consistency, LITE…

The subsumption problem with respect to terminologies in the description logic ALC is EXPTIME-complete. We investigate the computational complexity of fragments of this problem by means of allowed Boolean operators. Hereto we make use of…

We describe the development of a logic for reasoning about specifications in the Edinburgh Logical Framework (LF). In this logic, typing judgments in LF serve as atomic formulas, and quantification is permitted over contexts and terms that…

We explore the consequences of layering a Lambek proof system over an arbitrary (constraint) logic. A simple model-theoretic semantics for our hybrid language is provided for which a particularly simple combination of Lambek's and the proof…

Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained…

While the reasoning capabilities of Large Language Models (LLMs) excel in analytical tasks such as mathematics and code generation, their utility for abstractive summarization remains widely assumed but largely unverified. To bridge this…

We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…

The characterisation of termination using well-founded monotone algebras has been a milestone on the way to automated termination techniques, of which we have seen an extensive development over the past years. Both the semantic…

We introduce APPL (Abstract Program Property Logic), a unifying Hoare-style logic that subsumes standard Hoare logic, incorrectness logic, and several variants of Hyper Hoare logic. APPL provides a principled foundation for abstract program…

The field of implicit complexity has recently produced several bounded-complexity programming languages. This kind of language allows to implement exactly the functions belonging to a certain complexity class. We here present a…