Relevance logic

Non-classical logic | Paraconsistent logic | Substructural logic

Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. It is generally, but not universally, called relevant logic by British and, especially, Australian logicians, and relevance logic by American logicians. Relevance logic aims to capture aspects of implication that are ignored by the "material implication" operator in classical truth-functional logic, namely the notion of relevance between antecedent and conditional of a true implication. This idea is not new: C. I. Lewis was led to invent modal logic, and specifically strict implication, on the grounds that classical logic grants paradoxes of material implication such as the principle that a falsehood implies any proposition. Hence "if I'm a donkey, then two and two is four" is true when translated as a material implication, yet it seems intuitively false since a true implication must tie the antecedent and consequent together by some notion of relevance. And whether or not the speaker is a donkey seems in no way relevant to whether two and two is four. How does relevance logic formally capture a notion of relevance? In terms of a syntactical constraint for a propositional calculus, it is necessary, but not sufficient, that premises and conclusion share atomic formulae (formulae that do not contain any logical connectives). In a predicate calculus, relevance requires sharing of variables and constants between premises and conclusion. This can be ensured (along with stronger conditions) by, e.g., placing certain restrictions on the rules of a natural deduction system. In particular, a Fitch-style natural deduction can be adapted to accommodate relevance by introducing tags at the end of each line of an application of an inference indicating the premises relevant to the conclusion of the inference. Gentzen-style sequent calculi can be modified by removing the weakening rules that allow for the introduction of arbitrary formulae on the right or left side of the sequents. A notable feature of relevance logics is that they are paraconsistent logics: the existence of a contradiction will not cause "explosion". This follows from the fact that a conditional with a contradictory antecedent that does not share any propositional or predicate letters with the consequent cannot be true (or derivable). (Wikipedia).

Relevance model 1: Bernoulli sets vs. multinomial urns

[http://bit.ly/RModel] Relevance model is the language model of the relevant class. In this video we look at the difference between the multinomial model (the one used in relevance models) and the multiple-Bernoulli model, which forms the basis for the classical probabilistic models.

From playlist IR18 Relevance Model

Relevance model 4: Bayesian interpretation

[http://bit.ly/RModel] Another way to interpret the relevance model is via Bayesian estimation: the relevance model could be one of a large set of urns. We know what the urns are, but don't know which one is correct, so we compute the posterior probability for each candidate urn, and combi

From playlist IR18 Relevance Model

Relevance model 5: summary of assumptions

[http://bit.ly/RModel] The relevance model ranking is based on the probability ranking principle (PRP). It uses the background (corpus) model as a language model for the non-relevant class (just like the classical model), but has a novel estimate for the relevance model. The estimate is ba

From playlist IR18 Relevance Model

Evaluation 5: relevance judgments

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Relevance model 2: the sampling game

[http://bit.ly/RModel] How can we estimate the language model of the relevant class if we have no examples of relevant documents? We play a sampling game as follows. The relevance model is an urn with unknown parameters. We draw several samples from it and observe the query. What is the pr

From playlist IR18 Relevance Model

Relevance model 7: ranking functions

[http://bit.ly/RModel] The probability ranking principle (PRP) seems like the obvious ranking function for relevance models, but when we use it in the form of the odds ratio (as in the classical model), we bias our rankings towards the wrong type of document. A better approach is to use th

From playlist IR18 Relevance Model

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Relevance logic

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