arXiv subjects

Sajad Nazari

Publications and source records attributed to Sajad Nazari.

4 recordsLinked to original sources

arXiv2023

Reasoning with belief functions over Belnap--Dunn logic

We design an expansion of Belnap--Dunn logic with belief and plausibility functions that allow non-trivial reasoning with inconsistent and incomplete probabilistic information. We also formalise reasoning with non-standard probabilities and belief functions in two ways. First, using a calculus of linear inequalities, akin to the one presented in~\cite{FaginHalpernMegiddo1990}. Second, as a two-layered modal logic wherein reasoning with evidence (the outer layer) utilises paraconsistent expansions of Łukasiewicz logic. The second approach is inspired by~\cite{BaldiCintulaNoguera2020}. We prove completeness for both kinds of calculi and show their equivalence by establishing faithful translations in both directions.

math.LO↗

arXiv2022

Updating belief functions over Belnap--Dunn logic

Belief and plausibility are weaker measures of uncertainty than that of probability. They are motivated by the situations when full probabilistic information is not available. However, information can also be contradictory. Therefore, the framework of classical logic is not necessarily the most adequate. Belnap-Dunn logic was introduced to reason about incomplete and contradictory information. Klein et al and Bilkova et al generalize the notion of probability measures and belief functions to Belnap-Dunn logic, respectively. In this article, we study how to update belief functions with new pieces of information. We present a first approach via a frame semantics of Belnap-Dunn logic.

cs.AI↗

arXiv2020

How to reason with inconsistent probabilistic information?

A recent line of research has developed around logics of belief based on evidence. The approach of Bílková et al understands belief as based on information confirmed by a reliable source. We propose a finer analysis of how belief can be based on information, where the confirmation comes from multiple possibly conflicting sources and is of a probabilistic nature. We use Belnap-Dunn logic and its probabilistic extensions to account for potentially contradictory information on which belief is grounded. We combine it with an extension of Lukasiewicz logic, or a bilattice logic, within a two-layer modal logical framework to account for belief.

cs.LO↗

arXiv2020

Rough concepts

The present paper proposes a novel way to unify Rough Set Theory and Formal Concept Analysis. Our method stems from results and insights developed in the algebraic theory of modal logic, and is based on the idea that Pawlak's original approximation spaces can be seen as special instances of enriched formal contexts, i.e. relational structures based on formal contexts from Formal Concept Analysis.

cs.LO↗