相关论文: A connection method for a defeasible extension of …
We axiomatize the provability logic of $\HA$ and prove its decidability. Furthermore, we axiomatize the preservativity and relative admissibility relations for several modal logics extending iK4. A principal technical tool is the…
The Lambek calculus is a well-known logical formalism for modelling natural language syntax. The original calculus covered a substantial number of intricate natural language phenomena, but only those restricted to the context-free setting.…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
In this work we present a computation paradigm based on a concurrent and incremental construction of proof nets (de-sequentialized or graphical proofs) of the pure multiplicative and additive fragment of Linear Logic, a resources conscious…
We study complete approximations of an ontology formulated in a non-Horn description logic (DL) such as $\mathcal{ALC}$ in a Horn DL such as~$\mathcal{EL}$. We provide concrete approximation schemes that are necessarily infinite and observe…
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…
Causal discovery seeks to uncover causal relations from data, typically represented as causal graphs, and is essential for predicting the effects of interventions. While expert knowledge is required to construct principled causal graphs,…
The database community lacks a unified relational query language for subset selection and optimisation queries, limiting both user expression and query optimiser reasoning about such problems. Decades of research (latterly under the rubric…
In this paper we consider the most common ABox reasoning services for the description logic $\mathcal{DL}\langle \mathsf{4LQS^{R,\!\times}}\rangle(\mathbf{D})$ ($\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$, for short) and prove their…
Assessing ways in which Language Models can reduce their hallucinations and improve the outputs' quality is crucial to ensure their large-scale use. However, methods such as fine-tuning on domain-specific data or the training of a separate…
We introduce a generic extension of the popular branching-time logic CTL which refines the temporal until and release operators with formal languages. For instance, a language may determine the moments along a path that an until property…
Abduction in description logics finds extensions of a knowledge base to make it entail an observation. As such, it can be used to explain why the observation does not follow, to repair incomplete knowledge bases, and to provide possible…
The EL family of Description Logics (DLs) has been the subject of interest in recent years. On the one hand, these DLs are tractable, but fairly inexpressive. On the other hand, these DLs can be used for designing different classes of…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
We investigate the descriptional complexity of limited propagating Lindenmayer systems and their deterministic and tabled variants with respect to the number of rules and the number of symbols. We determine the decrease of complexity when…
We provide a new realisability model based on orthogonality for the multiplicative fragment of linear logic, both in presence of generalised axioms (MLL*) and in the standard case (MLL). The novelty is the definition of cut elimination for…
We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the…
This work, shows how propositional resolution can be generalized to obtain a resolution proof system for constrained pseudo-propositional logic (CPPL), which is an extension resulted from inserting the natural numbers with few constraints…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
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…