Related papers: Multiple-valued Logics
The way experts manage uncertainty usually changes depending on the task they are performing. This fact has lead us to consider the problem of communicating modules (task implementations) in a large and structured knowledge based system…
In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for…
In the paper, the idea of describing not-yet-verified properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the following two foundational problems of many-valued quantum logic…
Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…
This paper studies knowledge representation in multi-agent environment. We investigate technique for computation truth-values of statements based at a new temporal, agent's-knowledge logic TL. A logical language, mathematical symbolic…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
The evaluation of Large Language Models (LLMs) on mathematical reasoning has largely focused on elementary problems, competition-style questions, or formal theorem proving, leaving graduate-level and computational mathematics relatively…
Since the introduction of strong anticipation by D.~Dubois the numerous investigations of concrete systems have been proposed. In proposed paper the new examples of discrete dynamical systems with anticipation are considered. The…
Following {\L}ukasiewicz, we argue that future non-certain events should be described with the use of many-valued, not 2-valued logic. The Greenberger-Horne-Zeilinger `paradox' is shown to be an artifact caused by unjustified use of…
This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of…
Despite the massive advancements in large language models (LLMs), they still suffer from producing plausible but incorrect responses. To improve the reliability of LLMs, recent research has focused on uncertainty quantification to predict…
Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…
Intuitionistic Propositional Logic is proved to be an infinitely many valued logic by Kurt G\"odel (1932), and it is proved by Stanis{\l}aw Ja\'skowski (1936) to be a countably many valued logic. In this paper, we provide alternative proofs…
We investigate some well-known (and a few not-so-well-known) many-valued logics that have a small number (3 or 4) of truth values. For some of them we complain that they do not have any \emph{logical} use (despite their perhaps having some…
The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…
The paper presents some steps for multi-valued representation of neutrosophic information. These steps are provided in the framework of multi-valued logics using the following logical value: true, false, neutral, unknown and saturated.…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
As large language models (LLMs) are increasingly deployed in high-stakes applications, robust uncertainty estimation is essential for ensuring the safe and trustworthy deployment of LLMs. We present the most comprehensive study to date of…
In this paper we develop a 2-valued reduction of many-valued logics, into 2-valued multi-modal logics. Such an approach is based on the contextualization of many-valued logics with the introduction of higher-order Herbrand interpretation…