Related papers: G\"odel Mirror: A Formal System For Contradiction-…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
This paper explores the semantics of a combinatory fragment of reFLect, the lambda-calculus underlying a functional language used by Intel Corporation for hardware design and verification. ReFLect is similar to ML, but has a primitive data…
For half a century, authors have weakened the rule of necessitation in various more or less ad hoc ways in order to make inconsistent systems consistent. More recently, necessitation was weakened in a systematic way, not for the purpose of…
MerLean-Prover is an end-to-end Lean4 theorem prover that replaces sorry declarations with kernel-checkable proofs. It is built from three agent types (Planning, Check, and Lean) composed by a recursive outer loop whose unit of revision is…
This paper is devoted to systematic studies of some extensions of first-order G\"odel logic. The first extension is the first-order rational G\"odel logic which is an extension of first-order G\"odel logic, enriched by countably many…
We derive an intuitionistic version of G\"odel-L\"ob modal logic ($\sf{GL}$) in the style of Simpson, via proof theoretic techniques. We recover a labelled system, $\sf{\ell IGL}$, by restricting a non-wellfounded labelled system for…
Goedel's explicit thesis was that his undecidable formula GUS is a well-formed, well-defined formal sentence in any formalisation of Intuitive Arithmetic IA in which the axioms and rules of inference are recursively definable. His implicit…
This paper addresses the resilience of large-scale closed-loop structured systems in the sense of arbitrary pole placement when subject to failure of feedback links. Given a structured system with input, output, and feedback matrices, we…
Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
Robust perception and reasoning require consistency across sensory modalities. Yet current multimodal models often violate this principle, yielding contradictory predictions for visual and textual representations of the same concept. Rather…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
An ultimate universal theory -- a complete theory that accounts, via few and simple first principles, for all the phenomena already observed and that will ever be observed -- has been, and still is, the aspiration of most physicists and…
In the era of Vision-Language Models (VLMs), enhancing multimodal reasoning capabilities remains a critical challenge, particularly in handling ambiguous or complex visual inputs, where initial inferences often lead to hallucinations or…
Self-Consistency, a widely-used decoding strategy, significantly boosts the reasoning capabilities of Large Language Models (LLMs). However, it depends on the plurality voting rule, which focuses on the most frequent answer while…
Large language models (LLMs) with Chain-of-Thought (CoT) reasoning have achieved strong performance across diverse tasks, including mathematics, coding, and general reasoning. A distinctive ability of these reasoning models is…
When a cognitive system modifies its own functioning, what exactly does it modify: a low-level rule, a control rule, or the norm that evaluates its own revisions? Cognitive science describes executive control, metacognition, and…
This paper presents a Prolog-based reasoning module to generate counterfactual explanations given the predictions computed by a black-box classifier. The proposed symbolic reasoning module can also resolve what-if queries using the…