Related papers: A survey of paraconsistent logics

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…

We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…

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…

Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…

The AGM model is the most remarkable framework for modeling belief revision. However, it is not perfect in all aspects. Paraconsistent belief revision, multi-agent belief revision and non-prioritized belief revision are three different…

Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…

The paper investigates from a proof-theoretic perspective various non-contractive logical systems circumventing logical and semantic paradoxes. Until recently, such systems only displayed additive quantifiers (Gri\v{s}in, Cantini). Systems…

We present some hypersequent calculi for all systems of the classical cube and their extensions with axioms $T$, $P$, $D$, and, for every $n\geq 1$, rule $RD^+_n$. The calculi are internal as they only employ the language of the logic, plus…

When proving theorems from large sets of logical assertions, it can be helpful to restrict the search for a proof to those assertions that are relevant, that is, closely related to the theorem in some sense. For example, in the Watson…

The present paper constructs three new systems of clarithmetic (arithmetic based on computability logic --- see http://www.cis.upenn.edu/~giorgi/cl.html): CLA8, CLA9 and CLA10. System CLA8 is shown to be sound and extensionally complete…

Large language models have demonstrated impressive performance across a variety of reasoning tasks. However, their problem-solving ability often declines on more complex tasks due to hallucinations and the accumulation of errors within…

This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…

This paper considers KLM-style preferential non-monotonic reasoning in the setting of propositional team semantics. We show that team-based propositional logics naturally give rise to cumulative non-monotonic entailment relations. Motivated…

Following the lines of the analysis done in [BPZ07, BCF07] for first-order G\"odel logics, we present an analogous investigation for Nilpotent Minimum logic NM. We study decidability and reciprocal inclusion of various sets of first-order…

We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding…

Large language models (LLMs), such as LLaMA, Alpaca, Vicuna, GPT-3.5 and GPT-4, have advanced the performance of AI systems on various natural language processing tasks to human-like levels. However, their generalisation and robustness when…

We study the notion of conservative translation between logics introduced by Feitosa and D'Ottaviano. We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set…

In this paper I show, with a rich and systematized diet of examples, that many contra-classical logics can be presented as variants of FDE, obtained by modifying at least one of the truth or falsity conditions of some connective. Then I…

In this paper, we introduce a foundation for computable model theory of rational Pavelka logic (an extension of {\L}ukasiewicz logic) and continuous logic, and prove effective versions of some theorems in model theory. We show how to reduce…

We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions.…