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Despite significant efforts towards extending the AGM paradigm of belief change beyond finitary logics, the computational aspects of AGM have remained almost untouched. We investigate the computability of AGM contraction on non-finitary…
As LLMs advance their reasoning capabilities about the physical world, the absence of rigorous benchmarks for evaluating their ability to generate scientifically valid physical models has become a critical gap. Computational mechanics,…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Aiming to harmonise finite and infinite model reasoning, we initiate the study of partially finite models, where the reasoning task comes with a formula that specifies a part of the model that must be finite. We focus on the problem of…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
We introduce Nominal Matching Logic (NML) as an extension of Matching Logic with names and binding following the Gabbay-Pitts nominal approach. Matching logic is the foundation of the $\mathbb{K}$ framework, used to specify programming…
Cognitive BASIC is a minimal, BASIC-style prompting language and in-model interpreter that structures large language model (LLM) reasoning into explicit, stepwise execution traces. Inspired by the simplicity of retro BASIC, we repurpose…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs.…
Rule-based machine translation is more data efficient than the big data-based machine translation approaches, making it appropriate for languages with low bilingual corpus resources -- i.e., minority languages. However, the rule-based…
Joint logical-numerical reasoning remains a major challenge for language models, yet existing datasets rely on fixed rule sets and offer limited control over task complexity, constraining their generalizability for evaluation and training.…
The ability to manipulate logical-mathematical symbols (LMS), encompassing tasks such as calculation, reasoning, and programming, is a cognitive skill arguably unique to humans. Considering the relatively recent emergence of this ability in…
Recent advances in large language models have demonstrated impressive capabilities in mathematical formalization. However, existing benchmarks focus on logical verification of declarative propositions, often neglecting the task of…
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…
Language models (LMs) are often expected to generate strings in some formal language; for example, structured data, API calls, or code snippets. Although LMs can be tuned to improve their adherence to formal syntax, this does not guarantee…
Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
Computational argumentation has become an essential tool in various domains, including law, public policy, and artificial intelligence. It is an emerging research field in natural language processing that attracts increasing attention.…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
Genuine spatial reasoning relies on the capacity to construct and manipulate coherent internal spatial representations, often conceptualized as mental models, rather than merely processing surface linguistic associations. While large…