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  1. 1. Computational Issues in Calculi of Partial Inductive Definitions

    Författare :Per Kreuger; RISE; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Theory of computation; algorithms; logic; proof-theory; partial inductive defi-nitions; definitional reflection; disunification; closure; completion; negation; constructive negation; quantification; logic programming; meta programming; quantification; skolemization; self-reference; program semantics; declarative control; proof-search; theorem-proving.;

    Sammanfattning : We study the properties of a number of algorithms proposed to explore the computational space generated by a very simple and general idea: the notion of a mathematical definition and a number of suggested formal interpretations ofthis idea. Theories of partial inductive definitions (PID) constitute a class of logics based on the notion of an inductive definition. LÄS MER

  3. 2. A Natural Interpretation of Classical Proofs

    Författare :Jens Brage; Per Martin-Löf; Sara Negri; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Brouwer-Heyting-Kolmogorov; classical logic; constructive type theory; constructive semantics; proof interpretation; double-negation; continuation-passing-style; natural deduction; sequent calculus; cut elimination; explicit substitution; Mathematical logic; Matematisk logik;

    Sammanfattning : In this thesis we use the syntactic-semantic method of constructive type theory to give meaning to classical logic, in particular Gentzen's LK.We interpret a derivation of a classical sequent as a derivation of a contradiction from the assumptions that the antecedent formulas are true and that the succedent formulas are false, where the concepts of truth and falsity are taken to conform to the corresponding constructive concepts, using function types to encode falsity. LÄS MER