[PDF] Top 20 PP 2006 08: Modal Logics of Space

... substantial logics for significant spa- tial structures have been ...of modal logic, culminating in his proof with McKinsey that the simple decidable modal logic S4 is complete for interpreting ... See full document

... Throughout this paper we have made remarks contrasting the construction method to its more established counterpart, model theoretic approach to proving topological completeness. However, thus far we have only sketched ... See full document

... 6. Basic cardinality results about locally compact Hausdorff spaces In this section we present basic cardinality results about locally compact Hausdorff spaces that will be utilized in Section 7. In what follows we will ... See full document

... monotonic modal logics which are well-known for normal modal ...normal modal logics, more or less as presented in Blackburn et alii [6], which also accounts for most of the notation and ... See full document

... topological space is any pair (X, O), where O is a family of subsets of X containing the empty set and X itself, which is closed under finite intersections and arbitrary ...than space, including patterns of ... See full document

... Another fibre of the logic-geometry link is topos theory. Alexander Grothendieck invented toposes as a generalisation of topological spaces, to deal with the numerous situations occurring in mathematics which involve ... See full document

... We say that a formula φ is CS −LP satisfiable if there is a weak LP model that meets CS in which φ is true at some state. Similarly for CS-valid. Actually, Fitting considers two versions of his semantics (weak models and ... See full document

... Epistemic logics (i.e. the family of modal logics concerned with what an epistemic agent believes or knows) has by now a well-established semantics in the form of Kripke frames ... See full document

... the modal operators 2 and 3 in topological spaces as the interior and closure operators, then the complete modal logic of all topological spaces is S4 (McKinsey and Tarski ...complete modal logic of ... See full document

... (2). Let X be a K4-space. It is sufficient to show that X | = p ! ⌃ p i↵ X | = ( ), ( ). Suppose X 6| = ( ) or X 6| = ( ). Then there is a topo-rooted closed up-set Y of X and a stable map from Y onto or . Observe ... See full document

... The logics that we have studied in this paper fit into a more general en- ...for modal logic is its lattice of deductive systems such as K, S4, S5 or ...in Modal Logic”, CSLI and FOLLi). Among the ... See full document

... of modal logic came from philosophy, and dealt with such topics as modality, knowledge, conditionals, and ...to modal logics of time, space, or ...made modal logic even more ...(for ... See full document

... The motivation for such a project originally came from proof complexity. In particular, the semantics that are found and exposed can be used to pursue lower bounds on the length of proofs in propositional intuitionistic ... See full document

... these logics for practical ...Minkowski space-time, as it is the basis of Einstein’s theory of relativity and hence has practical application in reality, we discuss here branching structures of arbitrary ... See full document

... where the formula at the end may contain new free variables. BF is undecidable, but it has applications in arithmetic and set theory, as a way of defining 'absolute' properties not affected by the difference between ... See full document

... basic modal logic is enriched with the slash notation familiar from IF first-order logics, and the resulting logic is interpreted in terms of games and uniform ...IF modal logics. Within the ... See full document

... Negotiation between autonomous agents over the allocation of resources has become a central topic in AI. In this paper, we present some first steps towards using (modal) logic to model negotiation scenarios. We ... See full document

... Finding uniform axiomatizations for si-logics and modal logics has been a significant problem in the area. First general results in this direction were obtained by Jankov [17, 18], de Jongh [9], and ... See full document

... E is the smallest classical modal logic. The logic EN extends E by adding the axiom scheme > . Completeness holds for EN with respect neighborhood frames that contain the unit, i.e. for all w ∈ W, W ∈ N (w) ... See full document

... Abstract. Counterpart semantics is proposed as the appropriate semantical frame- work for a foundational investigation of quantified modal logics. It turns out to be a limit case of the categorical ... See full document