Neighborhoods, Ultrafilters, and Canonicity
نویسنده
چکیده
This paper will remind the reader of neighborhood semantics for modal logics, compare them with relational semantics, and then look at some questions about neighborhood semantics that have been answered, and some which are still open. We will then introduce “ultrafilter semantics,” a way of expressing all sets over a canonical frame in an ‘effable’ way. This provides us with a conceptually easy way of dispatching some questions about intensional logics. In particular, we show that all non-iterative intensional logics are canonical and we go on to indicate how we can use ultrafilter semantics to demonstrate the canonicity of the Sahlqvist Logics. Neighborhoods, Ultrafilters, and Canonicity Timothy J. Surendonk
منابع مشابه
Expressing Sets With Ultrafilters and the Canonicity of the Sahlqvist Logics
This paper will look at Sahlqvist’s theorem in a new way. We introduce and investigate a “skewed” type of semantics for modal logics over their canonical frames. We will use this semantics, to describe every subset of a canonical frame, we will show that the semantics respects all Sahlqvist formulae, and we then conclude that the Sahlqvist logics are canonical. This will be accomplished without...
متن کاملON SOFT ULTRAFILTERS
In this paper, the concept of soft ultrafilters is introduced and some of the related structures such as soft Stone-Cech compactification, principal soft ultrafilters and basis for its topology are studied.
متن کاملCanonicity Effect on Sentence Processing of Persian-speaking Broca’s Patients
Introduction: Fundamental notions of mapping hypothesis and canonicity were scrutinized in Persian-speaking aphasics. Methods: To this end, the performance of four age-, education-, and gender matched Persian-speaking Broca's patients and eight matched healthy controls in diverse complex structures were compared via the conduction of two tasks of syntactic comprehension and grammaticality jud...
متن کاملGenerated topology on infinite sets by ultrafilters
Let $X$ be an infinite set, equipped with a topology $tau$. In this paper we studied the relationship between $tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.
متن کاملHypercanonicity, Extensive Canonicity, Canonicity and Strong Completeness of Intermediate Propositional Logics
A b s t r a c t. Canonicity and strong completeness are well-established notions in the literature of intermediate propositional logics. Here we propose a more refined classification about canonicity distinguishing some subtypes of canonicity, we call hypercanonicity and extensive canonicity. We provide some semantical criteria for the classification of logics according to these notions and we ...
متن کامل