منابع مشابه
A Note on Rule-Finding Abduction
The rulending abduction is an abduction which begins with the observation of a surprising fact, nds a rule in the set of programs, and proposes a hypothesis. This paper investigates such rulending abduction for logic programming from two viewpoints: termination and analogical reasoning. In order to discuss the termination of rulending abduction, we introduce two concepts of loop-pair and loop-e...
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It is well–known (due to C. Parsons) that the extension of primitive recursive arithmetic PRA by first–order predicate logic and the rule of Π02–induction Π02–IR is Π 0 2–conservative over PRA. We show that this is no longer true in the presence of function quantifiers and quantifier–free choice for numbers AC– qf. More precisely we show that T :=PRA + Π02–IR+AC –qf proves the totality of the A...
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In this paper, we prove that certain theories of (many-sorted) intuitionistic predicate logic is closed under the independence of premiss rule (IPR). As corollaries, we show that HA and HA extended by some non-classical axioms and non-constructive axioms are closed under IPR.
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In this note we show that the so-called weakly extensional arithmetic in all finite types, which is based on a quantifier-free rule of extensionality due to C. Spector and which is of significance in the context of Gödel’s functional interpretation, does not satisfy the deduction theorem for additional axioms. This holds already for Π1axioms. Previously, only the failure of the stronger deducti...
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ژورنال
عنوان ژورنال: Historia Mathematica
سال: 1991
ISSN: 0315-0860
DOI: 10.1016/0315-0860(91)90499-n