Related papers: Towards a Logic for Reasoning About LF Specificati…
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions,…
Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
On the Semantic Web, metadata and ontologies are used to enable computers to read data. The Web Ontology Language (OWL) has been proposed as a standard ontological language, and various inference systems for this language have been studied.…
The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…
This paper offers an approach to extensible knowledge representation and reasoning for a family of formalisms known as Description Logics. The approach is based on the notion of adding new concept constructors, and includes a heuristic…
The language of epistemic specifications and epistemic logic programs extends disjunctive logic programs under the stable model semantics with modal constructs called subjective literals. Using subjective literals, it is possible to check…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
We present a theory of parameterized dynamic logic, namely DLp, for specifying and reasoning about a rich set of program models based on their transitional behaviours. Different from most dynamic logics that deal with regular expressions or…
We introduce a logical framework for the specification and verification of component-based systems, in which finitely many component instances are active, but the bound on their number is not known. Besides specifying and verifying…
We introduce a methodology and framework for expressing general preference information in logic programming under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and…
We introduce a new nameless representation of lambda terms inspired by ordered logic. At a lambda abstraction, number and relative position of all occurrences of the bound variable are stored, and application carries the additional…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
The approach to reasoning about structural operational semantics style specifications supported by the Abella system is discussed. This approach uses lambda tree syntax to treat object language binding and encodes binding related properties…
Large Language Models (LLMs) are increasingly integrated into the software engineering ecosystem. Their test-time compute (TTC) reasoning capabilities show significant potential for understanding program logic and semantics beyond mere…
A framework and methodology---termed LogiKEy---for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and…
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…