Sentence examples for semantic proof from inspiring English sources

Realization theorems have been proved syntactically, though presumably a semantic proof would also work.

In turn, strong models can be used to give a semantic proof of the Realization Theorem (cf. Section 4).

In this connection a simple semantic proof of the Second Incompleteness Theorem, which Kripke attributes to Kuratowski, might be worth mentioning.

Weak and strong completeness theorems are provable using the same machinery that applied in the case of \ \textsf{J}\), and a semantic proof of a Realization Theorem connecting \(\mathsf{JT}\) and \({\textsf{T}}\) is also available.

We end this consideration of the Second Incompleteness Theorem by noting that there are semantic proofs of consistency of course.

The proof-theoretic strength of a number of constructive and intuitionistic set theories has been established by a variety of tools, like, for example, an extension to set theory of the double negation interpretation (originated in (Friedman 1973a)), and a variety of other proof-theoretic interpretations, often resulting from a careful combination of semantic and proof theoretic techniques.

In fact, as is common in intuitionistic settings, a plethora of semantic and proof-theoretic methods are available for the study of constructive and intuitionistic set theories.

Starting from the major approaches to valid reasoning in standard logic (semantic and proof-theoretic), we consider variations with a richer vocabulary (e.g., modalities, generalized quantifiers), as well as genuine deviations from the classical paradigm, with their linguistic or scientific motivations (e.g., intuitionistic logic, linear logic).

Argument games have been found useful as a means of modelling dialectical discourse and in providing semantic bases for proof theoretic aspects of reasoning.

"GFZ ISDC: Semantic Web-based proof-of-concept platform".

Recall that the motivation for Field to use the compactness theorem was to reformulate conservativeness without having to assume abstract entities (namely, those required by the semantic and the proof-theoretic accounts of consistency).