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Reasoning is a fundamental capability of AI agents. Recently, large language models (LLMs) have shown remarkable abilities to perform reasoning tasks. However, numerous evaluations of the reasoning capabilities of LLMs have also showed some…
Large Language Models (LLMs) have significantly impacted nearly every domain of human knowledge. However, the explainability of these models esp. to laypersons, which are crucial for instilling trust, have been examined through various…
Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…
We study the problem of learning linear temporal logic (LTL) formulas from examples, as a first step towards expressing a property separating positive and negative instances in a way that is comprehensible for humans. In this paper we…
In this paper, we present a general realizability semantics for the simply typed $\lambda\mu$-calculus. Then, based on this semantics, we derive both weak and strong normalization results for two versions of the $\lambda\mu$-calculus…
This paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one…
Interpretability has become a necessary feature for machine learning models deployed in critical scenarios, e.g. legal system, healthcare. In these situations, algorithmic decisions may have (potentially negative) long-lasting effects on…
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…
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…
The point of this work is to explore axiomatisations of concurrent computation using the technology of proof theory and realizability. To deal with this problem, we redefine the Concurrent Realizability of Beffara using as realizers a…
The lack of interpretability has hindered the large-scale adoption of AI technologies. However, the fundamental idea of interpretability, as well as how to put it into practice, remains unclear. We provide notions of interpretability based…
Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…
Large Language Models (LLMs) have been recently proposed for supporting domain modeling tasks mostly related to the completion of partial models by recommending additional model elements. However, there are many more modeling tasks, one of…
In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining its correctness by fully characterizing the problems that are…
Mechanism design has long been a cornerstone of economic theory, with traditional approaches relying on mathematical derivations. Recently, automated approaches, including differentiable economics with neural networks, have emerged for…
Proof equivalence in a logic is the problem of deciding whether two proofs are equivalent modulo a set of permutation of rules that reflects the commutative conversions of its cut-elimination procedure. As such, it is related to the…
We introduce proof nets for PiL, an extension of first-order multiplicative additive linear logic with new operators allowing a shallow encoding of processes in the {\pi}-calculus as formulas. We provide correctness criterion,…
A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…
Propositional and modal inclusion logic are formalisms that belong to the family of logics based on team semantics. This article investigates the model checking and validity problems of these logics. We identify complexity bounds for both…
The black-box nature of Large Language Models necessitates novel evaluation frameworks that transcend surface-level performance metrics. This study investigates the internal neural representations of cognitive complexity using Bloom's…