Logic and Foundations Commons^™

Further Generalization Of N-D Distance And N-D Dependent Function In Extenics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Prof. Cai Wen [1] defined the 1-D Distance and 1-D Dependent Function in 1983. F. Smarandache [6] generalized them to n-D Distance and n-D Dependent Function respectively in 2012 during his postdoc research at Guangdong University of Technology in Guangzhou. O. I. Şandru [7] extended the last results in 2013. Now [2015], as a further generalization, we unify all these results into a single formula for the n-D Distance and respectively for the n-D Dependent Function.

Single Valued Neutrosophic Information Systems Based On Rough Set Theory, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The theory of rough sets was firstly proposed by Pawlak. Later on, Smarandache introduced the concept of neutrosophic (NS) sets in 1998. In this paper based on the concept of rough neutrosohic set, we define the concept of single valued neutrosophic information systems. In addition, we will discuss the knowledge reduction and extension of the single valued neutrosophic information systems.

Observing, Reporting, And Deciding In Networks Of Sentences, H. Jerome Keisler, Jeffrey M. Keisler

Jeffrey Keisler

In prior work we considered networks of agents who prove facts from their knowledge bases and report them to their neighbors in their common languages in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any decider's sentence that can be proved from the combined knowledge base. This paper introduces a more general setting where new observations may be added to knowledge bases and the decider must choose a sentence from a set of alternatives. We consider the question of when …

Ancestor Worship In The Logic Of Games. How Foundational Were Aristotle's Contributions?, John Woods

Baltic International Yearbook of Cognition, Logic and Communication

Notwithstanding their technical virtuosity and growing presence in mainstream thinking, game theoretic logics have attracted a sceptical question: "Granted that logic can be done game theoretically, but what would justify the idea that this is the preferred way to do it?'' A recent suggestion is that at least part of the desired support might be found in the Greek dialectical writings. If so, perhaps we could say that those works possess a kind of foundational significance. The relation of being foundational for is interesting in its own right. In this paper, I explore its ancient applicability to relevant, paraconsistent and …

Games And Logic, Gabriel Sandu

Baltic International Yearbook of Cognition, Logic and Communication

The idea behind these games is to obtain an alternative characterization of logical notions cherished by logicians such as truth in a model, or provability (in a formal system). We offer a quick survey of Hintikka's evaluation games, which offer an alternative notion of truth in a model for first-order langauges. These are win-lose, extensive games of perfect information. We then consider a variation of these games, IF games, which are win-lose extensive games of imperfect information. Both games presuppose that the meaning of the basic vocabulary of the language is given. To give an account of the linguistic conventions …

Constructive Type Theory And The Dialogical Approach To Meaning, Shahid Rahman, Nicolas Clerbout

Baltic International Yearbook of Cognition, Logic and Communication

In its origins Dialogical logic constituted one part of a new movement called the Erlangen School or Erlangen Constructivism. Its goal was to provide a new start to a general theory of language and of science. According to the Erlangen-School, language is not just a fact that we discover, but a human cultural accomplishment whose construction reason can and should control. The resulting project of intentionally constructing a scientific language was called the Orthosprache-project. Unfortunately, the Orthosprache-project was not further developed and seemed to fade away. It is possible that one of the reasons for this fading away is that …

Ludics, Dialogue And Inferentialism, Alain Lecomte

Baltic International Yearbook of Cognition, Logic and Communication

In this paper, we try to show that Ludics, a (pre-)logical framework invented by J-Y. Girard, enables us to rethink some of the relationships between Philosophy, Semantics and Pragmatics. In particular, Ludics helps to shed light on the nature of dialogue and to articulate features of Brandom's inferentialism.

Argumentation And Inference: A Unified Approach, Christophe Fouqueré, Myriam Quatrini

Baltic International Yearbook of Cognition, Logic and Communication

We propose in this paper to use Ludics as a unified framework for the analysis of dialogue and the reasoning system. Not only is Ludics a logical theory, but it may also be built by means of concepts of game theory. We first present the main concepts of Ludics. A design is an abstraction and a generalization of the concept of proof. Interaction between designs is equivalent to cut elimination or modus ponens in logical theories. It appears to be a natural means for representing dialogues and also for reasoning. A design is a set of sequences of alternate actions …

Antilogic, Benoît Castelnérac, Mathieu Marion

Baltic International Yearbook of Cognition, Logic and Communication

This paper is an interim report of joint work begun in (Castelnérac & Marion 2009) on dialectic from Parmenides to Aristotle. In the first part we present rules for dialectical games, understood as a specific form of antilogikê developed by philosophers, and explain some of the key concepts of these dialectical games in terms of ideas from game semantics. In the games we describe, for a thesis A asserted by the answerer, a questioner must elicit the answerer’s assent to further assertions B₁, B₂,…, B_n, which form a scoreboard from which the questioner seeks …

Trust And Risk In Games Of Partial Information, Robin Clark

Baltic International Yearbook of Cognition, Logic and Communication

Games of partial information have been used to explicate Gricean implicature; their solution concept has been murky, however. In this paper, I will develop a simple solution concept that can be used to solve games of partial information, depending on the players' mutual trust and tolerance for risk. In addition, I will develop an approach to non-conventional quantity implicatures that relies on "face" (Goffman (1967), Brown and Levinson (1987)).

Relation Between Hilbert Algebras And Be–Algebras, A. Rezaei, A. B. Saeid, R. A. Borzooei

Applications and Applied Mathematics: An International Journal (AAM)

Hilbert algebras are introduced for investigations in intuitionistic and other non - classical logics and BE -algebra is a generalization of dual BCK -algebra. In this paper, we investigate the relationship between Hilbert algebras and BE -algebras. In fact, we show that a commutative implicative BE -algebra is equivalent to the commutative self distributive BE -algebra, therefore Hilbert algebras and commutative self distributive BE -algebras are equivalent.

Hyperbolic Geometry And God, Andrew Lazowski

Presidential Seminar on the Catholic Intellectual Tradition

Development of hyperbolic geometry --Fifth axiom is a problem --Model of the divine --Infinite power --Infinite knowledge --Infinite benevolence.

Examples Where The Conjunctive And Dempster’S Rules Are Insensitive, Florentin Smarandache, Jean Dezert, Valeri Kroumov

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present several counter-examples to the Conjunctive rule and to Dempster rule of combinations in information fusion.

Borel Complexity Of The Isomorphism Relation For O-Minimal Theories, Davender Singh Sahota '99

Doctoral Dissertations

In 1988, Mayer published a strong form of Vaught's Conjecture for o-minimal theories (1). She showed Vaught's Conjecture holds, and characterized the number of countable models of an o-minimal theory T if T has fewer than 2K ° countable models. Friedman and Stanley have shown in (2) that several elementary classes are Borel complete. This work addresses the class of countable models of an o-minimal theory T when T has 2N ° countable models, including conditions for when this class is Borel complete. The main result is as follows.

Theorem 1. Let T be an o-minimal theory in a countable …

Relation Lifting, With An Application To The Many-Valued Cover Modality, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jirí Velebil

Engineering Faculty Articles and Research

We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the existence of a distributive law of T over the “powerset monad” on categories, one is the preservation by T of “exactness” of certain squares. Both characterisations are generalisations of the “classical” results known for set functors: the first characterisation generalises the existence of a distributive law over the genuine powerset monad, the second generalises preservation of weak pullbacks.

The results presented in this paper …

A Reduction Theorem For The Kripke-Joyal Semantics: Forcing Over An Arbitrary Category Can Always Be Replaced By Forcing Over A Complete Heyting Algebra, Imants Barušs, Robert Woodrow

Psychology

No abstract provided.

Fuzzy Neutrosophic Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, authors give the notion of different neutrosophic models like, neutrosophic cognitive maps (NCMs), neutrosophic relational maps (NEMs), neutrosophic relational equations (NREs), neutrosophic bidirectional associative memories (NBAMs) and neutrosophic associative memories (NAMs) for socio scientists. This book has six chapters. The first chapter introduces the basic concepts of neutrosophic numbers and notions about neutrosophic graphs which are essential to construct these neutrosophic models. In chapter two we describe the concept of neutrosophic matrices and the essential operations related with them which are used in the study and working of these neutrosophic models. However the reader must be familiar …

Correlation Coefficient Of Interval Neutrosophic Set, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce for the first time the concept of correlation coefficients of interval valued neutrosophic set (INS for short). Respective numerical examples are presented.

Dynamic Sequent Calculus For The Logic Of Epistemic Actions And Knowledge, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano

Engineering Faculty Articles and Research

"Dynamic Logics (DLs) form a large family of nonclassical logics, and perhaps the one enjoying the widest range of applications. Indeed, they are designed to formalize change caused by actions of diverse nature: updates on the memory state of a computer, displacements of moving robots in an environment, measurements in models of quantum physics, belief revisions, knowledge updates, etc. In each of these areas, DL-formulas express properties of the model encoding the present state of affairs, as well as the pre- and post-conditions of a given action. Actions are semantically represented as transformations of one model into another, encoding the …

Nominal Regular Expressions For Languages Over Infinite Alphabets, Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto

Engineering Faculty Articles and Research

We propose regular expressions to abstractly model and study properties of resource-aware computations. Inspired by nominal techniques – as those popular in process calculi – we extend classical regular expressions with names (to model computational resources) and suitable operators (for allocation, deallocation, scoping of, and freshness conditions on resources). We discuss classes of such nominal regular expressions, show how such expressions have natural interpretations in terms of languages over infinite alphabets, and give Kleene theorems to characterise their formal languages in terms of nominal automata.