Related papers: LD Double Logic and Gamma-LD Existential Graphs
I use the Pythia scaling suite (Biderman et al. 2023) to investigate if and how two well-known polarity illusions, the NPI illusion and the depth charge illusion, arise in LLMs. The NPI illusion becomes weaker and ultimately disappears as…
A graph is a fundamental data model to represent various entities and their complex relationships in society and nature, such as social networks, transportation networks, and financial networks. Recently, large language models (LLMs) have…
The adoption of Large Language Models (LLMs) is rapidly expanding across various tasks that involve inherent graphical structures. Graphs are integral to a wide range of applications, including motion planning for autonomous vehicles,…
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…
We discuss the definability of finite graphs in first-order logic with two relation symbols for adjacency and equality of vertices. The logical depth $D(G)$ of a graph $G$ is equal to the minimum quantifier depth of a sentence defining $G$…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
The shift from monolithic LLMs to distributed multi-agent architectures demands new frameworks for verifying and securing autonomous coordination. Unlike traditional multi-agent systems focused on cooperative state alignment, modern LLM…
This paper presents a formal theory which describes propositional binary logic as a semantically closed formal language, and allows for syntactically and semantically well-formed formulae, formal proofs (demonstrability in Hilbertian…
HyLL (Hybrid Linear Logic) and SELL (Subexponential Linear Logic) are logical frameworks that have been extensively used for specifying systems that exhibit modalities such as temporal or spatial ones. Both frameworks have linear logic (LL)…
Two lines of approaches are adopted for complex reasoning with LLMs. One line of work prompts LLMs with various reasoning structures, while the structural outputs can be naturally regarded as intermediate reasoning steps. Another line of…
The present work aims to give a unity of logic via standard sequential, unpolarized games. Specifically, our vision is that there must be mathematically precise concepts of linear refinement and intuitionistic restriction of logic such that…
Answering questions over domain-specific graphs requires a tailored approach due to the limited number of relations and the specific nature of the domain. Our approach integrates classic logical programming languages into large language…
Large language models (LLMs) are a promising venue for natural language understanding and generation. However, current LLMs are far from reliable: they are prone to generating non-factual information and, more crucially, to contradicting…
Large language models (LLMs) exhibit logically inconsistent hallucinations that appear coherent yet violate reasoning principles, with recent research suggesting an inverse relationship between causal reasoning capabilities and such…
The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions…
To appear in Theory and Practice of Logic Programming (TPLP). In this paper we propose an extension of logic programming (LP) where each default literal derived from the well-founded model is associated to a justification represented as an…
For a graph $G$, the $\gamma$-graph of $G$, $G(\gamma)$, is the graph whose vertices correspond to the minimum dominating sets of $G$, and where two vertices of $G(\gamma)$ are adjacent if and only if their corresponding dominating sets in…
A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTTO and LTTO*, which we claim correspond closely to the classical predicative…
Probabilistic logic reasoning is a central component of such cognitive architectures as OpenCog. However, as an integrative architecture, OpenCog facilitates cognitive synergy via hybridization of different inference methods. In this paper,…
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…