
46SecondOrder Quantifier Elimination in HigherOrder Contexts with Applications to the Semantical Analysis of ConditionalsStudia Logica 87 (1): 3750. 2007.Secondorder quantifier elimination in the context of classical logic emerged as a powerful technique in many applications, including the correspondence theory, relational databases, deductive and knowledge databases, knowledge representation, commonsense reasoning and approximate reasoning. In the current paper we first generalize the result of Nonnengart and Szałas [17] by allowing secondorder variables to appear within higherorder contexts. Then we focus on a semantical analysis of conditio…Read more

75Fuzzy logics based on [0,1)continuous uninormsArchive for Mathematical Logic 46 (56): 425449. 2007.Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the halfopen real unit interval [0,1), generalizing the continuous tnorm based approach of Hájek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0,1] whose monoid operations are uninorms continuous on [0,1). Several extensions of BUL are also introduced. In particular, Cross ratio logic CRL, is shown to be complete with respect to one special …Read more

32Voting by Eliminating QuantifiersStudia Logica 92 (3): 365379. 2009.Mathematical theory of voting and social choice has attracted much attention. In the general setting one can view social choice as a method of aggregating individual, often conflicting preferences and making a choice that is the best compromise. How preferences are expressed and what is the “best compromise” varies and heavily depends on a particular situation. The method we propose in this paper depends on expressing individual preferences of voters and specifying properties of the resulting ra…Read more

44Modal Logics of Reactive FramesStudia Logica 93 (2): 405446. 2009.A reactive graph generalizes the concept of a graph by making it dynamic, in the sense that the arrows coming out from a point depend on how we got there. This idea was first applied to Kripke semantics of modal logic in [2]. In this paper we strengthen that unimodal language by adding a second operator. One operator corresponds to the dynamics relation and the other one relates paths with the same endpoint. We explore the expressivity of this interpretation by axiomatizing some natural subclass…Read more

20A normal logic that is complete for neighborhood frames but not for Kripke framesTheoria 40 (3): 148153. 1974.

19Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: OverviewStudia Logica 93 (23): 357381. 2009.In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks 6, then this attack can itself be attacked by another node c. This attack itself can attack another node d. This situation can be iterated to any level with attacks and nodes attacking other attacks and other nodes. In this paper we provide semantics to such networks. We offer three different approaches to obtaining semantics. 1. The translation approach This uses the methodology of ' …Read more

36Handbook of the History and Philosophy of Logic, vol. 10: Inductive Logic (edited book)Elsevier. forthcoming.