# Nonmonotonic and Paraconsistent Reasoning: From Basic Entailments to Plausible Relations

@inproceedings{Arieli1999NonmonotonicAP, title={Nonmonotonic and Paraconsistent Reasoning: From Basic Entailments to Plausible Relations}, author={Ofer Arieli and Arnon Avron}, booktitle={ESCQARU}, year={1999} }

In this paper we develop frameworks for logical systems which are able to reflect not only nonmonotonic patterns of reasoning, but also paraconsistent reasoning. For this we consider a sequence of generalizations of the pioneering works of Gabbay, Kraus, Lehmann, Magidor and Makinson. Our sequence of frameworks culminates in what we call plausible, nonmonotonic, multiple-conclusion consequence relations (which are based on a given monotonic one). Our study yields intuitive justifications for…

## 8 Citations

General Patterns for Nonmonotonic Reasoning: From Basic Entailments to Plausible Relations

- Computer ScienceLog. J. IGPL
- 2000

A sequence of generalizations of the pioneering works of Gabbay, Kraus, Lehmann, Magidor and Makinson are considered, which allow the use of monotonic nonclassical logics as the underlying logic upon which nonmonotonic reasoning may be based.

Unifying logics via context-sensitiveness

- Computer ScienceJ. Log. Comput.
- 2017

The cut-elimination theorem is proved for a version of controlled propositional classical logic, i.e. the sequent calculus for classical propositional logic to which a suitable system of control sets is applied.

Reasoning with different levels of uncertainty

- Computer ScienceJ. Appl. Non Class. Logics
- 2003

A family of preferential logics that are useful for handling information with different levels of uncertainty are introduced, and it is shown that the formalisms in this family can be embedded in corresponding four-valued logics with at most three uncertainty levels.

Minimally inconsistent reasoning in Semantic Web

- Computer Science, PhilosophyPloS one
- 2017

This paper presents a non-monotonic paraconsistent version of description logic reasoning, called minimally inconsistent reasoning, where inconsistencies tolerated in the reasoning are minimized so that more reasonable conclusions can be inferred.

Preferential Logics for Reasoning with Graded Uncertainty

- Computer ScienceECSQARU
- 2003

A family of preferential logics that are useful for handling information with different levels of uncertainty are introduced and any formalism in this family that is based on a well-founded ordering of the different types of uncertainty, can be embedded in a corresponding four-valued logic with at most three uncertainty levels.

Reasoning with Modularly Pointwise Preferential Relations

- Computer Science

A family of preferential consequence relations is introduced, deened by a simple and natural many-valued semantics, that share many desirable properties for common-sense reasoning, such as paraconsistency.

Useful adaptive logics for rational and paraconsistent reasoning

- Philosophy
- 2000

A family of logics that are particularly useful for reasoning with uncertainty are introduced, which are nonmonotonic, para-consistent, adaptive in the sense of Batens, plausibility logics in thesense of Lehmann, and rational in the Sense of Lehman and Magidor.

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