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Pré-Publication, Document De Travail Année : 2022

The contextual logic

Arnaud Kohler
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Résumé

Many researchers in Artificial Intelligence today consider that human reasoning cannot be modelled by “one” formal language. Given its complexity and diversity, observed in the context of work done in cognitive science, it would even be possible that it escapes formal logic. Many convincing arguments have been put forward, and the various failures in this field suffered by logicians during the 20th century reinforce this conclusion. However, failures and arguments are not proof. We show in this article, through a concrete example, that it would be premature to bury the historical ambition of logic. It presents a formalism, noted Lc, which we call contextual logic. This remains strictly and scrupulously within the framework of the syntax of propositional logic. The set of atomic propositions is extended by what we call thoughts. They appear automatically and silently and carry the semantic interpretation function. This is defined by the analysis of the behaviour of the thoughts in the models of the theory. The originality of Lc is to model a totally fallibilistic and perspectivistic reasoning: "Each piece of knowledge is uncertain. Belief is built by aggregating the different justifiable points of view, accepting the possibility that they are incomplete, incorrect, or inconsistent with each other". In contrast to the principle of proof inherited from mathematics, Lc models that nothing is provable, and adopts the principle of non-refutability to meet the need for decidability. Contextual logic captures notions of inconsistency, predicate, and epistemic modality, accepts abductive and inductive reasoning, and solves belief revision and epistemic rooting problems in a radical way.
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Dates et versions

hal-03195162 , version 1 (10-04-2021)
hal-03195162 , version 2 (21-05-2021)
hal-03195162 , version 3 (16-10-2021)
hal-03195162 , version 4 (21-01-2022)
hal-03195162 , version 5 (18-04-2022)
hal-03195162 , version 6 (02-10-2022)
hal-03195162 , version 7 (29-10-2022)

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  • HAL Id : hal-03195162 , version 5

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Arnaud Kohler. The contextual logic. 2022. ⟨hal-03195162v5⟩
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