The notion of acceptability is a counterpart of the phenomenon observed in our daily argumentation and originates from an old saying, “The one who has the last word laughs best”, as stated by Dung. It is an empirical social truth or wisdom that has been evolved in various cultural sphere over generations and considered useful by people. It is remarkable and suggestive that Dung’s theory of argu...

We give several new applications of the wreath product of forest algebras to the study of logics on trees. These include new simplified proofs of necessary conditions for definability in CTL and first-order logic with the ancestor relation; a sequence of identities satisfied by all forest languages definable in PDL; and new examples of languages outsideCTL, along with an application to the ques...

Let L be a countable first-order language and M = (M, . . .) be an L-structure. “Definable set” means a subset of M which is L-definable in M with parameters. A set X ⊆ M is said to be immune if it is infinite and does not contain any infinite definable subset. X is said to be partially immune if for some definable A, A∩X is immune. X is said to be totally non-immune if for every definable A, A...

This paper gives an overview and an analysis of representative vowel space depictions found in the phonetic literature of the past four centuries. A visual representation of 24 selected structural proposals with time is given in poster form, after translation to a common notation. A first-order approach is developed by which the distance between any pair of vowel schemes may be measured. Using ...

The study of classes of models of a finite diagram was initiated by S. Shelah in 1969. A diagram D is a set of types over the empty set, and the class of models of the diagram D consists of the models of T which omit all the types not in D. In this work, we introduce a natural dependence relation on the subsets of the models for the No-stable case which share many of the formal properties of fo...

The paper has a form of a survey on basics of logical geometry and consists of three parts. It is focused on the relationship between many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on important model-theoretic concepts. Our aim is to show that both approaches go in parallel and there are bridges which allow to transfer results, notions and problems bac...