Related papers: Abductive Reasoning in a Paraconsistent Framework
In real-world applications, knowledge bases consisting of all the information at hand for a specific domain, along with the current state of affairs, are bound to contain contradictory data coming from different sources, as well as data…
A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of…
Logics closed under classes of substitutions broader than class of uniform substitutions are known as hyperformal logics. This paper extends known results about hyperformal logics in two ways. First: we examine a very powerful form of…
Large language models demonstrate strong reasoning capabilities through chain-of-thought prompting, but whether this reasoning quality transfers across languages remains underexplored. We introduce a human-validated framework to evaluate…
We introduce a logical framework for reasoning about "uncertain interpretations" and investigate two key applications: a new semantics for implication capturing a kind of "meaning entailment", and a conservative notion of "evidentially…
The aim of this paper is to introduce the logics FFDE and FN4, which are universally free versions of Belnap-Dunn's four-valued logic, also known as the logic of first-degree entailment (FDE), and Nelson's paraconsistent logic QN4 (N-).…
Logical systems with classical negation and means for sentential or propositional self-reference involve, in some way, paradoxical statements such as the liar. However, the paradox disappears if one replaces classical by an appropriate…
We address the problem of propositional logic-based abduction, i.e., the problem of searching for a best explanation for a given propositional observation according to a given propositional knowledge base. We give a general algorithm, based…
When people share the same documents and observations yet reach different conclusions, the disagreement often shifts into a judgment that the other party is cognitively defective, irrational, or acting in bad faith. This paper argues that…
Word puzzles and the problem of their representations in logic languages have received considerable attention in the last decade (Ponnuru et al. 2004; Shapiro 2011; Baral and Dzifcak 2012; Schwitter 2013). Of special interest is the problem…
We show that language models hallucinate not because they fail to detect uncertainty, but because of a failure to integrate it into output generation. Across architectures, uncertain inputs are reliably identified, occupying…
Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover,…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
This paper undertakes a foundational inquiry into logical inferentialism with particular emphasis on the normative standards it establishes and the implications these pose for classical logic. The central question addressed herein is: 'What…
The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity (or impredicativity) of second and higher order…
This study intends to systematically disentangle pure logic reasoning and text understanding by investigating the contrast across abstract and contextualized logical problems from a comprehensive set of domains. We explore whether LLMs…
Deduction, induction, and abduction are fundamental reasoning paradigms, core for human logical thinking. Although improving Large Language Model (LLM) reasoning has attracted significant research efforts, the extent to which the…
Counterfactual reasoning, a hallmark of intelligence, consists of three steps: inferring latent variables from observations (abduction), constructing alternatives (interventions), and predicting their outcomes (prediction). This skill is…