Related papers: Reasoning about Algebraic Data Types with Abstract…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
We give a procedure that can be used to automatically satisfy invariants of a certain shape. These invariants may be written with the operations intersection, composition and converse over binary relations, and equality over these…
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…
What does it mean for an algebraic rewrite rule to subsume another rule (that may then be called a subrule)? We view subsumptions as rule morphisms such that the simultaneous application of a rule and a subrule (i.e. the application of a…
Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall…
Reasoning in large language models is predominantly evaluated through labeled benchmarks, conflating task performance with the quality of internal inference. Here we study reasoning as an intrinsic dynamical process by examining the…
We present a novel general resource analysis for logic programs based on sized types.Sized types are representations that incorporate structural (shape) information and allow expressing both lower and upper bounds on the size of a set of…
It is argued that a broad class of AGI-relevant algorithms can be expressed in a common formal framework, via specifying Galois connections linking search and optimization processes on directed metagraphs whose edge targets are labeled with…
Metamodeling refers to scenarios in ontologies in which classes and roles can be members of classes or occur in roles. This is a desirable modelling feature in several applications, but allowing it without restrictions is problematic for…
We introduce algebraic machine reasoning, a new reasoning framework that is well-suited for abstract reasoning. Effectively, algebraic machine reasoning reduces the difficult process of novel problem-solving to routine algebraic…
In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology, which can be formulated in a description logic (DL) or using existential rules. In the literature, there…
Large language models (LLMs) are increasingly used for tasks that implicitly reduce to Boolean satisfiability (SAT), yet their reasoning ability on SAT remains unclear. We present a systematic study of LLMs on 2-SAT and 3-SAT, together with…
There is a wide gap between symbolic reasoning and deep learning. In this research, we explore the possibility of using deep learning to improve symbolic reasoning. Briefly, in a reasoning system, a deep feedforward neural network is used…
Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…
Robots assisting humans in complex domains have to represent knowledge and reason at both the sensorimotor level and the social level. The architecture described in this paper couples the non-monotonic logical reasoning capabilities of a…
W.C. Rounds and G.-Q. Zhang (2001) have proposed to study a form of disjunctive logic programming generalized to algebraic domains. This system allows reasoning with information which is hierarchically structured and forms a (suitable)…
We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…
In this paper we provide for parsing with respect to grammars expressed in a general TFS-based formalism, a restriction of ALE. Our motivation being the design of an abstract (WAM-like) machine for the formalism, we consider parsing as a…
Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly…
In functional programming languages, generalized algebraic data types (GADTs) are very useful as the unnecessary pattern matching over them can be ruled out by the failure of unification of type arguments. In dependent type systems, this is…