Intuitionistic completeness of first-order logic
نویسندگان
چکیده
منابع مشابه
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...
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...
متن کاملConceptual 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...
متن کاملFirst-Order Logic, Second-Order Logic, and Completeness
Both firstand second-order logic (FOL and SOL, respectively) as we use them today were arguably created by Frege in his Begriffsschrift – if we ignore the notational differences. SOL also suggests itself as a natural, and because of its much greater strength, desirable extension of FOL. But at least since W. V. Quine’s famous claim that SOL is “set theory in sheep’s clothing” it is widely held ...
متن کاملTopological Completeness of First-order Modal Logic
As McKinsey and Tarski [19] showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for (classical) propositional modal logic, in which the “necessity” operation is modeled by taking the interior of an arbitrary subset of a topological space. The topological interpretation was extended by Awodey and Kishida [3] in a natural ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2014
ISSN: 0168-0072
DOI: 10.1016/j.apal.2013.07.009