Zero-one laws with respect to models of provability logic and two Grzegorczyk logics

It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. Therefore, many properties of models, such as having an even number of elements, cannot be expressed in the language of first-order logic. Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5 and for frames corresponding to S4 and S5. In this paper, we prove zero-one laws for provability logic and its two siblings Grzegorczyk logic and weak Grzegorczyk logic, with respect to model validity. Moreover, we axiomatize validity in almost all relevant finite models, leading to three different axiom systems

NIDUS IDEARUM. Scilogs, IV: vinculum vinculorum

Welcome into my scientific lab! My lab[oratory] is a virtual facility with non-controlled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings ground , opinion , expectation ), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this fourth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring mostly to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. Feel free to budge in or just use the scilogs as open source for your own ideas

Nidus idearum. Scilogs, III: Viva la Neutrosophia!

Welcome into my scientific lab! My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings ground , opinion , expectation ), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this third book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. Feel free to budge in or just use the scilogs as open source for your own ideas! * Neutrosophy is a new branch of philosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. I coined the words “neutrosophy” and “neutrosophic” in my 1998 book: Florentin Smarandache, Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998; http://fs.gallup.unm.edu/eBook-neutrosophics6.pdf (last edition online)

On similarity in fuzzy description logics

This paper is a contribution to the study of similarity relations between objects represented as attribute-value pairs in Fuzzy Description Logics . For this purpose we use concrete domains in the fuzzy description logic IALCEF(D)IALCEF(D) associated either with a left-continuous or with a finite t-norm. We propose to expand this fuzzy description logic by adding a Similarity Box (SBox) including axioms expressing properties of fuzzy equalities. We also define a global similarity between objects from similarities between the values of each object attribute (local similarities) and we prove that the global similarity defined using a t-norm inherits the usual properties of the local similarities (reflexivity, symmetry or transitivity). We also prove a result relative to global similarities expressing that, in the context of the logic MTL∀, similar objects have similar properties, being these properties expressed by predicate formulas evaluated in these object