Intensional Positive Set Theory
نویسنده
چکیده
Positive set theory is at present a subject on its own, from the initial work of R.J. Malitz [16], to the further developments including topological models [6], [7], and very strong variants, in particular Esser’s theory GPK ∞ where the class of all well-founded sets interprets ZF [3], [4]. In another direction, namely in languages allowing terms, does positive set theory appear as a weakening of partial set theory, linked to the concept of partial information; this actually follows the line initiated in Gilmore’s
منابع مشابه
Melvin Fitting Intensional Logic — Beyond First Order
Classical first-order logic can be extended in two different ways to serve as a foundation for mathematics: introduce higher orders, type theory, or introduce sets. As it happens, both approaches have natural analogs for quantified modal logics, both approaches date from the 1960’s, one is not very well-known, and the other is well-known as something else. I will present the basic semantic idea...
متن کاملConstructive Foundations for Z
The speciication language Z is based on classical logic and extensional set theory. These are mathematical choices which are largely independent of Z and its calculus of schemata. This paper explores the possibilities of replacing classical logic with intuitionistic logic and extensional set theory with intensional set theory, and some of the consequences of these changes for principles of prog...
متن کاملAn Intensional Schrödinger Logic
We investigate the higher-order modal logic SωI , which is a variant of the system Sω presented in our previous work. A semantics for that system, founded on the theory of quasi sets, is outlined. We show how such a semantics, motivated by the very intuitive base of Schrödinger logics, provides an alternative way to formalize some intensional concepts and features which have been used in recent...
متن کاملTowards a Unified Theory of Intensional Logic Programming
Intensional Logic Programming is a new form of logic programming based on intensional logic and possible-worlds semantics. Intensional logic allows us to use logic programming to specify nonterminating computations and to capture the dynamic aspects of certain problems in a natural and problem-oriented style. The meanings of formulas of an intensional firstorder language are given according to ...
متن کاملSymmetric Splitting in the General Theory of Stable Models
Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for smaller programs. This idea is extended here to the general theory of stable models that replaces traditional logic programs by arbitrary firstorder sentences and distinguishes between intensional and extensional predicates. We discuss two kinds of splitting: a set of intensional predicate...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Reports on Mathematical Logic
دوره 40 شماره
صفحات -
تاریخ انتشار 2006