Related papers: Tolerance and degrees of truth
The paper proposes a new type of negation in multi-valued logics, providing a different way to answer the following question: what does it mean that some object language formula does not have a given truth-value. Along the way, the paper…
Large language models have demonstrated impressive performance across many domains of mathematics and physics. One natural question is whether such models can support research in highly abstract theoretical fields such as quantum field…
People increasingly use large language models (LLMs) for everyday moral and interpersonal guidance, yet these systems cannot interrogate missing context and judge dilemmas as presented. We introduce a perturbation framework for testing the…
This paper discusses the merits and demerits of crisp logic and fuzzy logic with respect to their applicability in intelligent response generation by a human being and by a robot. Intelligent systems must have the capability of taking…
Large Language Models increasingly rely on self-explanations, such as chain of thought reasoning, to improve performance on multi step question answering. While these explanations enhance accuracy, they are often verbose and costly to…
Large language models (LLMs) achieve strong performance across many natural language processing tasks, yet their decision processes remain difficult to interpret. This lack of transparency creates challenges for trust, debugging, and…
In a recent paper as an alternative to models based on the notion of ideal mathematical point, characterized by a property of separatedness, we considered a viewpoint based on the notion of continuous change, making use of elements of a…
This paper addresses the logical and computational foundations of multi-step fuzzy inference using the Mamdani-Assilian type of fuzzy rules by implementing such inference in Goedel logic with truth constants. We apply the results achieved…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html ) is a research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been.…
Conformance checking techniques are widely adopted to pinpoint possible discrepancies between process models and the execution of the process in reality. However, state of the art approaches adopt a crisp evaluation of deviations, with the…
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$.…
In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices,…
We investigate the internal behavior of Transformer-based Large Language Models (LLMs) when they generate factually incorrect text. We propose modeling factual queries as constraint satisfaction problems and use this framework to…
There is knowledge. There is belief. And there is tacit agreement.' 'We may talk about objects. We may talk about attributes of the objects. Or we may talk both about objects and their attributes.' This work inspects tacit agreements on…
Multi-winner approval elections are seen in a variety of settings ranging from academic societies and associations to public elections. In such elections, it is often the case that ballot-length restrictions are enforced; that is, where…
We apply a framework developed by C. S. Peirce to analyze the concept of clarity, so as to examine a pair of rival mathematical approaches to a typical result in analysis. Namely, we compare an intuitionist and an infinitesimal approaches…
Algorithms and other formal models purportedly incorporating human values like fairness have grown increasingly popular in computer science. In response to sociotechnical challenges in the use of these models, designers and researchers have…
Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…
Sensitivity analysis informs causal inference by assessing the sensitivity of conclusions to departures from assumptions. The consistency assumption states that there are no hidden versions of treatment and that the outcome arising…
Large language models (LLMs) are increasingly used for tasks that implicitly reduce to Boolean satisfiability (SAT), yet their reasoning ability on SAT remains unclear. We present a systematic study of LLMs on 2-SAT and 3-SAT, together with…