Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tarski's relevance logic; Version 2   Tarski's relevance logic is defined and shown to contain many formulas and
derived rules of inference. The definition arises from Tarski's work on
first-order logic restricted to finitely many variables. It is a relevance
logic because it contains the Basic Logic of Routley-Plumwood-Meyer-Brady, has
Belnap's variable-sharing property, and avoids the paradoxes of implication. It
does not include several formulas used as axioms in the Anderson-Belnap system
$R$. For example, the Axiom of Contraposition is not in Tarski's relevance
logic. On the other hand, the Rules of Contraposition and Disjunctive Syllogism
are derived rules of inference in Tarski's relevance logic. It also contains a
formula (not previously known or considered as an axiom for any relevance
logic) that provides a counterexample to a completeness theorem of T. Kowalski
(that the system $R$ is complete with respect to the class of dense commutative
relation algebras).

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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat