kripke bas proposed a number of counteretxamples to the classic thesis, which ays that the class of necmary fropositions roincidn with the cla1ss of a priori ones. these counteretxamples involve some necessary a posten'ori trutbs as well as contingent a priori ones. om cfbis exmnplu far the loller is the 1ta11dard metre example. in thi1 paper, after presenting a brief sketch of kripke&apos...

Graded modal logic (GML) was originally presented by Kit Fine (1972) to make the modal analogue to counting quantifiers explicit. A graded modal formula ♦k is true at a state w in a Kripke model if there are at least k successor states of w where φ is true. One open problem in GML is to show a Goldblatt-Thomason theorem for it. See M. De Rijke’s notes (2000). Recently, Katsuhiko Sano and Minghu...

Alternative proofs for Guaspari and Solovay's completeness theorems for R are presented. R is an extension of the provability logic L and was developed in order to study the formal properties of the provability predicate of PA occurring in sentences that may contain connectives for witness comparison. (The primary example of sentences involving witness comparison is the Rosser sentence.) In thi...

Modal inclusion logic is the extension of basic modal logic with inclusion atoms, and its semantics is defined on Kripke models with teams. A team of a Kripke model is just a subset of its domain. In this paper we give a complete characterisation for the expressive power of modal inclusion logic: a class of Kripke models with teams is definable in modal inclusion logic if and only if it is clos...

The complexity of model checking branching and linear time temporal logics over Kripke structures has been addressed in e.g. [SC85, CES86]. In terms of the size of the Kripke model and the length of the formula, they show that the model checking problem is solvable in polynomial time for CTL and NP-complete for L(F ). The model checking problem can be generalised by allowing more succinct descr...

We consider the problem of the product nite model property for binary products of modal logics. First we give a new proof for the product nite model property of the logic of products of Kripke frames, a result due to Shehtman. Then we modify the proof to obtain the same result for logics of products of Kripke frames satisfying any combination of seriality, re exivity and symmetry. We do not con...

The objectives of this research are to further investigate the foundations for novel SMT and SAT-based bounded model checking (BMC) algorithms for real-time and multiagent systems. A major part of the research will involve the development of SMT-based BMC methods for standard Kripke structures, extended Kripke structures, and for different kinds of interpreted systems for different kinds of tem...