Conceptual completeness for first-order Intuitionistic logic: an application of categorical logic
نویسندگان
چکیده
منابع مشابه
Conceptual Completeness for First-Order Intuitionistic Logic: An Application of Categorical Logic
This paper concerns properties of interpretations between first-order theories in intuitionistic logic, and in particular how certain syntactic properties of such interpretations can be characterised by their model-theoretic properties. We allow theories written in possibly many-sorted languages. Given two such theories 3 and 7, an interpretation of 3 in 3’ will here mean a model of 3 in the ‘f...
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Intuitionistic Completeness of First-Order Logic
We establish completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable if and only if its embedding into minimal logic, mFOL, is uniformly valid under the Brouwer Heyting Kolmogorov (BHK) semantics, the intended semantics of iFOL and mFOL. Our proof is intuitionistic and provides an effective procedure Prf that converts uniform minimal evidence into a formal fi...
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By a strong conceptual completeness (XC) statement for a logical doctrine we mean an assertion that says that any theory of the doctrine can be recovered from an appropriate structure formed by the models of the theory. The expression ‘logical doctrine’ is used here as in [9] to mean a specific selection of logical operations giving rise to a notion of theory, in the form of a structured catego...
متن کاملIntuitionistic Completeness of First-Order Logic – mPC Case
We constructively prove in type theory the completeness of the minimal Propositional Calculus, showing that a formula is provable in mPC if and only if it is uniformly valid in constructive type theory extended with the intersection operator. Our completeness proof provides an effective procedure Prf that converts any uniform evidence into a formal an mPC proof. Mark Bickford has implemented Pr...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1989
ISSN: 0168-0072
DOI: 10.1016/0168-0072(89)90007-9