Related papers: Multiple-valued Logics

This paper builds on a recent article co-authored by the present author, H. Hosni and F. Montagna. It is meant to contribute to the logical foundations of probability theory on many-valued events and, specifically, to a deeper understanding…

The second edition of "Semantic Relations Between Nominals" by Vivi Nastase, Stan Szpakowicz, Preslav Nakov and Diarmuid \'O S\'eaghdha has been published in April 2021 by Morgan & Claypool…

In this paper we consider the class of truth-functional many-valued logics with a finite set of truth-values. The main result of this paper is the development of a new \emph{binary} sequent calculi (each sequent is a pair of formulae) for…

Large language models (LLMs) have shown strong capabilities, enabling concise, context-aware answers in question answering (QA) tasks. The lack of transparency in complex LLMs has inspired extensive research aimed at developing methods to…

In this paper two knowledge representation models are proposed, FP4 and FP6. Both combine ideas from fuzzy sets and four-valued and hexa-valued logics. Both represent imprecise properties whose accomplished degree is unknown or…

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…

Large Language Models (LLMs) have been transformative across many domains. However, hallucination, i.e., confidently outputting incorrect information, remains one of the leading challenges for LLMs. This raises the question of how to…

It is shown that the proof theory for sketches and forms provided in Part I of this paper (see http://www.cwru.edu/1/class/mans/math/pub/wells) is strong enough to produce all the theorems of the entailment system for multisorted equational…

In recent years, Large Language Models (LLMs) have become fundamental to a broad spectrum of artificial intelligence applications. As the use of LLMs expands, precisely estimating the uncertainty in their predictions has become crucial.…

As the capabilities of Large Language Models (LLMs) expand, it becomes increasingly important to evaluate them beyond basic knowledge assessment, focusing on higher-level language understanding. This study introduces MultiPragEval, the…

Uncertainty estimation is crucial for evaluating Large Language Models (LLMs), particularly in high-stakes domains where incorrect answers result in significant consequences. Numerous approaches consider this problem, while focusing on a…

Causal multiteam semantics is a framework where probabilistic dependencies arising from data and causation between variables can be together formalized and studied logically. We consider several logics in the setting of causal multiteam…

This is a manuscript to be published as a book chapter. The text summarizes some of my critics concerning Everett's theory as seen from the perspective of a Bohmian. This is the second draft and comments are still welcome.

We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…

Deep learning models are widely used for various industrial and scientific applications. Even though these models have achieved considerable success in recent years, there exists a lack of understanding of the rationale behind decisions…

We study many-valued coalgebraic logics with semi-primal algebras of truth-degrees. We provide a systematic way to lift endofunctors defined on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal…

Large Language Model (LLM) evaluation is currently one of the most important areas of research, with existing benchmarks proving to be insufficient and not completely representative of LLMs' various capabilities. We present a curated…

Despite the widespread adoption of large language models (LLMs) for recommendation, we demonstrate that LLMs often exhibit uncertainty in their recommendations. To ensure the trustworthy use of LLMs in generating recommendations, we…

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…

Complex multi-step reasoning tasks, such as solving mathematical problems, remain challenging for large language models (LLMs). While outcome supervision is commonly used, process supervision via process reward models (PRMs) provides…