Twenty Years of Topological Logic

نویسنده

  • Ian Pratt-Hartmann
چکیده

Topological logics are formal systems for representing and manipulating information about the topological relationships between objects in space. Over the past two decades, these logics have been the subject of intensive research in Artificial Intelligence, under the general rubric of Qualitative Spatial Reasoning. This chapter sets out the mathematical foundations of topological logics, and surveys some of their many surprising properties.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

G*-continuous Mappings in Intuitionistic Fuzzy Topological Spaces

After the introduction of fuzzy sets by Zadeh [15] in 1965 and fuzzy topology by chang [4] in 1967. Several researches were conducted on the generalizations of the notions of fuzzy sets and fuzzy topology. The concept of intuitionistic fuzzy sets was introduced by Atanassov [1] as a generalization of fuzzy sets . In the last 20 years various concepts of fuzzy mathematics have been extended for ...

متن کامل

Dynamic topological S5

The topological semantics for modal logic interprets a standard modal propositional language in topological spaces rather than Kripke frames: the most general logic of topological spaces becomes S4. But othermodal logics can be given a topological semantics by restricting attention to subclasses of topological spaces: in particular, S5 is logic of the class of almost discrete topological spaces...

متن کامل

Dynamic Topological Logic

Dynamic Topological Logic provides a context for studying the confluence of the topological semantics for S4, based on topological spaces rather than Kripke frames; topological dynamics; and temporal logic. In the topological semantics for S4, 2 is interpreted as topological interior: thus S4 can be understood as the logic of topological spaces. Topological dynamics studies the asymptotic prope...

متن کامل

Topological Completeness of First-Order Modal Logics

As McKinsey and Tarski [20] 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. This topological interpretation was recently extended in a natural way to arbitrary...

متن کامل

Generalizing Topology via Chu Spaces

By using the representational power of Chu spaces we define the notion of a generalized topological space (or GTS, for short), i.e., a mathematical structure that generalizes the notion of a topological space. We demonstrate that these topological spaces have as special cases known topological spaces. Furthermore, we develop the various topological notions and concepts for GTS. Moreover, since ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013