Simple completeness proofs for some spatial logics of the real line
نویسنده
چکیده
McKinsey–Tarski (1944), Shehtman (1999), and Lucero-Bryan (2011) proved completeness theorems for modal logics with modalities 2, 2 and ∀, and [∂] and ∀, respectively, with topological semantics over the real numbers. We give short proofs of these results using lexicographic sums of linear orders.
منابع مشابه
Truth Values and Connectives in Some Non-Classical Logics
The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...
متن کاملBuilding a Multi-Objective Model for Multi-Product Multi-Period Production Planning with Controllable Processing Times: A Real Case Problem
Model building is a fragile and complex process especially in the context of real cases. Each real case problem has its own characteristics with new concepts and conditions. A correct model should have some essential characteristics such as: being compatible with real conditions, being of sufficient accuracy, being logically traceable and etc. This paper discusses how to build an efficient mode...
متن کاملDensity Elimination and Rational Completeness for First-Order Logics
Density elimination by substitutions is introduced as a uniformmethod for removing applications of the Takeuti-Titani density rule from proofs in firstorder hypersequent calculi. For a large class of calculi, density elimination by this method is guaranteed by known sufficient conditions for cut-elimination. Moreover, adding the density rule to any axiomatic extension of a simple first-order lo...
متن کاملQuantified Multimodal Logics in Simple Type Theory
We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple experiments, using existing higher-order theorem provers, to demonstrate that the embedding allows automated proofs of statements in these logics, as well as meta pro...
متن کاملA modal logic framework for reasoning about comparative distances and topology
In 1944, McKinsey and Tarski proved that S4 is the logic of the topological interior and closure operators of any separable dense-in-itself metric space. Thus, the logic of topological interior and closure over arbitrary metric spaces coincides with the logic of the real line, the real plane, and any separable dense-in-itself metric space; it is finitely axiomatisable and PSpace-complete. Becau...
متن کامل