Introduction Rule

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Jurgen Dix - One of the best experts on this subject based on the ideXlab platform.

Nick Bassiliades - One of the best experts on this subject based on the ideXlab platform.

Miguel Lopez Astorga - One of the best experts on this subject based on the ideXlab platform.

  • the disjunction Introduction Rule syntactic and semantics considerations
    Pragmalingüística, 2015
    Co-Authors: Miguel Lopez Astorga
    Abstract:

    The mental logic theory claims that the disjunction Introduction Rule, which is a valid Rule in classic logic, is not a Rule naturally used by human mind. However, a study carried by Orenes and Johnson-Laird suggests that this theory is wrong because there are cases in which the disjunction Introduction Rule appears to be applied by individuals. Orenes and Johnson-Laird explain their results based on the mental models theory. Nevertheless, in this paper, I try to show that, if it is assumed that people recover, by means of a semantic analysis of possibilities, the real logical forms of propositions before using formal Rules, the mental logic theory can also explain the results achieved by Orenes and Johnson-Laird. Likewise, I include some comments on the possibility that both theories are complementary and related.

A S Troelstra - One of the best experts on this subject based on the ideXlab platform.

  • natural deduction for intuitionistic linear logic
    Annals of Pure and Applied Logic, 1995
    Co-Authors: A S Troelstra
    Abstract:

    Abstract The paper deals with two versions of the fragment with unit, tensor, linear implication and storage operator (the exponential!) of intuitionistic linear logic. The first version, ILL, appears in a paper by Benton, Bierman, Hyland and de Paiva; the second one, ILL+, is described in this paper. ILL has a contraction Rule and an Introduction Rule !I for the exponential; in ILL+, instead of a contraction Rule, multiple occurrences of labels for assumptions are permitted under certain conditions; moreover, there is a different Introduction Rule for the exponential, !I+, which is closer in spirit to the necessitation Rule for the normalizable version of S4 discussed by Prawitz in his monograph “Natural Deduction”. It is relatively easy to adapt Prawitz's treatment of natural deduction for intuitionistic logic to ILL+; in particular one can formulate a notion of strong validity (as in Prawitz's “Ideas and Results in Proof Theory”) permitting a proof of strong normalization. The conversion Rules for ILL explicitly mentioned in the paper by Benton et al. do not suffice for normal forms with subformula property, but we can show that this can be remedied by addition of a special permutation conversion plus some “satellite” permutation conversions. Some discussion of the categorical models which might correspond to ILL+ is given.

Guido Governatori - One of the best experts on this subject based on the ideXlab platform.