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

We present a new asynchronous model of computation named Stellar Resolution based on first-order unification. This model of computation is obtained as a formalisation of Girard's transcendental syntax programme, sketched in a series of…

Recent advances in reasoning-centric language models have highlighted reinforcement learning (RL) as a promising method for aligning models with verifiable rewards. However, it remains contentious whether RL truly expands a model's…

Strategy Logic (SL) is a logical formalism for strategic reasoning in multi-agent systems. Its main feature is that it has variables for strategies that are associated to specific agents with a binding operator. We introduce Graded Strategy…

This paper is a continuation of [arXiv:1603.02204]. Exploded layered tropical (ELT) algebra is an extension of tropical algebra with a structure of layers. These layers allow us to use classical algebraic results in order to easily prove…

We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…

Retrieval-augmented generation has gained significant attention due to its ability to integrate relevant external knowledge, enhancing the accuracy and reliability of the LLMs' responses. Most of the existing methods apply a dynamic…

Originating in Girard's Linear logic, Ehrhard and Regnier's Taylor expansion of $\lambda$-terms has been broadly used as a tool to approximate the terms of several variants of the $\lambda$-calculus. Many results arise from a Commutation…

Recent reports claim that Large Language Models (LLMs) have achieved the ability to derive new science and exhibit human-level general intelligence. We argue that such claims are not rigorous scientific claims, as they do not satisfy…

Large Language Models (LLMs), excel in natural language understanding, but their capability for complex mathematical reasoning with an amalgamation of structured tables and unstructured text is uncertain. This study explores LLMs'…

We expand FLew with a unary connective whose algebraic counterpart is the operation that gives the greatest complemented element below a given argument. We prove that the expanded logic is conservative and has the Finite Model Property. We…

Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…

We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate their systematic generalization abilities on a…

MLL proof equivalence is the problem of deciding whether two proofs in multiplicative linear logic are related by a series of inference permutations. It is also known as the word problem for star-autonomous categories. Previous work has…

Linear rules have played an increasing role in structural proof theory in recent years. It has been observed that the set of all sound linear inference rules in Boolean logic is already coNP-complete, i.e. that every Boolean tautology can…

We augment LP with a strong conditional operator, to yield a logic we call "strong LP," or LP=>. The resulting logic can speak of consistency in more discriminating ways, but introduces new possibilities for trivializing paradoxes.

We study the expressive power of various modal logics with team semantics. We show that exactly the properties of teams that are downward closed and closed under team k-bisimulation, for some finite k, are definable in modal logic extended…

In this paper, we give a new linear time correctness condition for proof nets of Multiplicative Linear Logic without units. Our approach is based on a rewriting system over trees. We have only three rewrite rules. Compared with previous…

In this paper we extend the notion of Melham sum to the Pell and Pell-Lucas sequences. While the proofs of general statements rely on the binomial theorem, we prove some spacial cases by the known Pell identities. We also give extensions of…

We study several extensions of linear-time and computation-tree temporal logics with quantifiers that allow for counting how often certain properties hold. For most of these extensions, the model-checking problem is undecidable, but we show…

Let T be an algebraically bounded theory. We consider the $L(\bar\delta)$-expansions of T by a tuple $\bar \delta$ of derivations (which may be commuting or not). We investigate the model completion of either of the above theories, whose…