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Ontology is a popular method for knowledge representation in different domains, including the legal domain, and description logics (DL) is commonly used as its description language. To handle reasoning based on inconsistent DL-based legal…
The formal system lambda-delta is a typed lambda calculus that pursues the unification of terms, types, environments and contexts as the main goal. lambda-delta takes some features from the Automath-related lambda calculi and some from the…
Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
Foundational verification considers the functional correctness of programming languages with formalized semantics and uses proof assistants (e.g., Coq, Isabelle) to certify proofs. The need for verifying complex programs compels it to…
Natural language reasoning plays an increasingly important role in improving language models' ability to solve complex language understanding tasks. An interesting use case for reasoning is the resolution of context-dependent ambiguity. But…
Dung's Abstract Argumentation Framework (AF) has emerged as a key formalism for argumentation in Artificial Intelligence. It has been extended in several directions, including the possibility to express supports, leading to the development…
This study empirically validates automated logical specification methods for behavioural models, focusing on their robustness, scalability, and reproducibility. By the systematic reproduction and extension of prior results, we confirm key…
Experiments require human decisions in the design process, which in turn are reformulated and summarized as inputs into a system (computational or otherwise) to generate the experimental design. I leverage this system to promote a language…
We propose an approach to formally specifying the behavioral properties of systems that rely on a perception model for interactions with the physical world. The key idea is to introduce embeddings -- mathematical representations of a…
This paper defines a language L for specifying LFG grammars. This enables constraints on LFG's composite ontology (c-structures synchronised with f-structures) to be stated directly; no appeal to the LFG construction algorithm is needed. We…
Algebraic specification has a long tradition in bridging the gap between specification and programming by making specifications executable. Building on extensive experience in designing, implementing and using specification formalisms that…
We give an algebraic characterization of the tree languages that are defined by logical formulas using certain Lindstr\"om quantifiers. An important instance of our result concerns first-order definable tree languages. Our characterization…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
Large Language Models (LLMs) excel in complex reasoning tasks but struggle with consistent rule application, exception handling, and explainability, particularly in domains like legal analysis that require both natural language…
We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…
A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…
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…
Reasoning in the Semantic Web (SW) commonly uses Description Logics (DL) via OWL2 DL ontologies, or SWRL for variables and Horn clauses. The Rule Interchange Format (RIF) offers more expressive rules but is defined outside RDF and rarely…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…