Related papers: Nexus Authorization Logic (NAL): Logical Results
Large language models (LLMs) commonly boost reasoning via sample-evaluate-ensemble decoders, achieving label free gains without ground truth. However, prevailing strategies score candidates using only external outputs such as token…
Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-wise behaviour of a system. Its quantified extensions allow…
We interpret Linear Logic Proof Nets in a term language based on Solos calculus. The system includes a synchronisation mechanism, obtained by a conservative extension of the logic, that enables to define non-deterministic behaviours and…
A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general…
The foundations of formal models for epistemic and doxastic logics often rely on certain logical aspects of modal logics such as S4 and S4.2 and their semantics; however, the corresponding mathematical results are often stated in papers or…
Despite significant progress in post-hoc explanation methods for neural networks, many remain heuristic and lack provable guarantees. A key approach for obtaining explanations with provable guarantees is by identifying a cardinally-minimal…
I show that the logic $\textsf{TJK}^{d+}$, one of the strongest logics currently known to support the naive theory of truth, is obtained from the Kripke semantics for constant domain intuitionistic logic by (i) dropping the requirement that…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
A simplified variant of G\"odel's ontological argument is presented. The simplified argument is valid already in basic modal logics K or KT, it does not suffer from modal collapse, and it avoids the rather complex predicates of essence…
Neural networks are one of the most investigated and widely used techniques in Machine Learning. In spite of their success, they still find limited application in safety- and security-related contexts, wherein assurance about networks'…
In the article we investigate three classes of extended Boolean Connexive Logics. Two of them are extensions of Modal and non-Modal Boolean Connexive Logics with a property of closure under an arbitrary number of negations. The remaining…
The Lax Logical Framework, LLFP, was introduced, by a team including the last two authors, to provide a conceptual framework for integrating different proof development tools, thus allowing for external evidence and for postponing,…
This paper belongs to the field of probabilistic modal logic, focusing on a comparative analysis of two distinct semantics: one rooted in Kripke semantics and the other in neighbourhood semantics. The primary distinction lies in the…
We present a Coq formalization of the Quantified Reflection Calculus with one modality, or $\mathsf{QRC}_1$. This is a decidable, strictly positive, and quantified modal logic previously studied for its applications in proof theory. The…
The development of artificial intelligence systems with advanced reasoning capabilities represents a persistent and long-standing research question. Traditionally, the primary strategy to address this challenge involved the adoption of…
We consider multi-agent argumentation, where each agent's view of the arguments is encoded as an argumentation framework (AF). Then we study deliberative processes than can occur on this basis. We think of a deliberative process as taking…
Natural language explanations (NLEs) are a special form of data annotation in which annotators identify rationales (most significant text tokens) when assigning labels to data instances, and write out explanations for the labels in natural…
In their recent paper (GandALF 2018), Goubault, Ledent, and Rajsbaum provided a formal epistemic model for distributed computing. Their logical model, as an alternative to the well-studied topological model, provides an attractive framework…
Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…
We investigate a logic for asynchronous announcements wherein the sending of the messages by the environment is separated from their reception by the individual agents. Both come with different modalities. In the logical semantics, formulas…