Related papers: Glueability of resource proof-structures: invertin…

In [Mon11] are studied, for the axiomatic extensions of the monoidal t-norm based logic ([EG01]), the properties of single chain completeness. On the other side, in [GJKO07, Chapter 5] are studied many logical and algebraic properties (like…

We develop and study the complexity of propositional proof systems of varying strength extending resolution by allowing it to operate with disjunctions of linear equations instead of clauses. We demonstrate polynomial-size refutations for…

The expansion method of Lie algebras by a semigroup or S-expansion is generalized to act directly on the group manifold, and not only at the level of its Lie algebra. The consistency of this generalization with the dual formulation of the…

Training Large Language Models (LLMs) with Group Relative Policy Optimization (GRPO) encounters a significant challenge: models often fail to produce accurate responses, particularly in small-scale architectures. This limitation not only…

We adapt a continuous logic axiomatization of tracial von Neumann algebras due to Farah, Hart and Sherman in order to prove a metatheorem for this class of structures in the style of proof mining, a research program that aims to obtain the…

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some…

We consider strong expansions of the theory of ordered abelian groups. We show that the assumption of strength has a multitude of desirable consequences for the structure of definable sets in such theories, in particular as relates to…

The profusion of knowledge encoded in large language models (LLMs) and their ability to apply this knowledge zero-shot in a range of settings makes them promising candidates for use in decision-making. However, they are currently limited by…

As large language models (LLMs) are increasingly used in Text-to-SQL tasks, Reinforcement Learning (RL) has become a common method for improving performance. Existing methods primarily rely on static execution feedback, which restricts…

The (extended) AGM postulates for belief revision seem to deal with the revision of a given theory K by an arbitrary formula, but not to constrain the revisions of two different theories by the same formula. A new postulate is proposed and…

We introduce a calculus of extensional resource terms. These are resource terms \`a la Ehrhard-Regnier, but in infinitely eta-long form. The calculus still retains a finite syntax and dynamics: in particular, we prove strong confluence and…

In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…

Recently, directly using large language models (LLMs) has been shown to be the most reliable method to evaluate QA models. However, it suffers from limited interpretability, high cost, and environmental harm. To address these, we propose to…

While large language models (LLMs) are proficient at question-answering (QA), it is not always clear how (or even if) an answer follows from their latent "beliefs". This lack of interpretability is a growing impediment to widespread use of…

Relationship is clarified between the notions of linear extension of algebraic theories, and central extension, in the sense of commutator calculus, of their models. Varieties of algebras turn out to be nilpotent Maltsev precisely when…

We study a new extension of the weak MSO logic, talking about boundedness. Instead of a previously considered quantifier U, expressing the fact that there exist arbitrarily large finite sets satisfying a given property, we consider a…

Parametric language models (LMs), which are trained on vast amounts of web data, exhibit remarkable flexibility and capability. However, they still face practical challenges such as hallucinations, difficulty in adapting to new data…

We develop a timeout based extension of propositional linear temporal logic (which we call TLTL) to specify timing properties of timeout based models of real time systems. TLTL formulas explicitly refer to a running global clock together…

For the sake of reliability, the kernels of Interactive Theorem Provers (ITPs) are generally kept relatively small. On top of the kernel, additional symbols and inference rules are defined. This paper presents an analysis of how kernel…

This work proposes a quantitative metric to analyze potential reusability of a BPEL (Business Process Execution Language) Process. The approach is based on Description and Logic Mismatch Probability of a BPEL Process that will be reused…