@article{2174056033554e68803feb854d5dc3b3,

title = "A tree-sequent calculus for a natural predicate extension of visser's propositional logic",

abstract = "We study predicate logic that is interpreted in Kripke models similarly to intuitionistic logic except that the accessibility relation of each model is not necessarily reflexive. Unlike in Ruitenburg's Basic Predicate Calculus, which is previous work on logic of this kind, the notion of formula in our system is the standard one in predicate logic. We give an axiomatization for this logic in the style of tree-sequent calculus (a special form of labelled sequent calculus) and prove its completeness with respect to the class of Kripke models.",

keywords = "Kripke models, Predicate logic, Tree-sequent calculus, Visser's propositional logic",

author = "Ryo Ishigaki and Kentaro Kikuchi",

note = "Funding Information: We are grateful to Ryo Kashima for giving us introductions to tree-sequent calculus and Ichiro Hasuo for his advice on drawing diagrams of tree-sequents using pstricks packages. We also thank the anonymous referee for useful comments. This research was partially supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Young Scientists (B) 17700003.",

year = "2007",

month = mar,

doi = "10.1093/jigpal/jzm004",

language = "English",

volume = "15",

pages = "149--164",

journal = "Logic Journal of the IGPL",

issn = "1367-0751",

publisher = "Oxford University Press",

number = "2",

}