DOCSLIB.ORG

Philosophy and Non-Classical Logics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Philosophy and Non-Classical Logics XVIII SLALM 16-20 December, 2019 Universidad de Concepi´on Concepi´on,CHILE http://slalmxviii.udec.cl PHILOSOPHY AND NON-CLASSICAL LOGICS Invited talks Nicolas Clerbout, The dialogical study of non-classical logics: dialogical pluralism in hindsight ......................................................... 3 Eduardo Alejandro Barrio, Substructural logics and matainferences. 4 Contributed talks Luis Felipe Bartolo Alegre, On falsifying empirical contradictions . 6 Leonardo Cano, A natural semantics for the pull-back of fiber bundles of structures . 7 J.-Mart´ınCastro-Manzano, Numerical term logic tableaux . 8 J.-Mart´ınCastro-Manzano, Distribution trees . 9 Pen´elope Cordero, Subdirectly irreducible complex c-PBL-algebras . 10 Lilian Cruz, Categorical equivalence between PMVf -product algebras and semi- low fu-rings................................................................. 11 Am´ılcarArroyo Medina and Sandra Dolores Cuenca, Dos cr´ıticas al monismo sobre la noci´onde consecuencia . 12 Sebastian E. Ferrando, Preferencias imprecisas como modelos neighborhood 13 Jos´eDavid Garc´ıa, Test modality as a connexive operator . 14 Noem´ıLubomirsky, The lattice of subvarieties of the variety of BL-algebras generated by [0; 1]MV ⊕ [0; 1]G ................................................ 16 Miguel Marcos, The twist structure of Nelson-type algebras . 17 Alba Massolo, Pluralism and normativity in logic . 18 Rodrigo Mena Gonz´alez, Sobre la traducibilidad de bases deductivas . 19 Eric Pezoa, Monismo o pluralismo en el anti excepcionalismo sobre la l´ogica . 20 Yuri Poveda, Mvw-rigs and product mv-algebras. 21 Hern´anSan Mart´ın, On the free frontal implicative semilattice extension of a frontal Hilbert algebra. 22 Sandra Visokolskis, Analogical proportion-based inferences within non-classical logic: historical variants of Aristotelian argumentative strategies . 23 Anya Yermakova, Non-classical logics of the late Russian Empire . 24 INVITED TALKS 2 I NICOLAS CLERBOUT, The dialogical study of non-classical logics: dialogical plural- ism in hindsight. Instituto de Filosof´ıa,Universidad de Valpara´ıso,Serrano 546 - Valpara´ıso,Chile. E-mail: [email protected]. The dialogical approach to logic is born at the end of the fifties from the work of P. Lorenzen. Inspired by Wittgenstein's meaning as use approach and mathematical game theory, the framework provides an alternative to the more widespread model- theoretical and proof-theoretical approaches. Initially, it was introduced in the context of constructive mathematics and logic. During the 90s and the 2000s, the framework has been developed and used for the study, comparison and combination of various logical systems [2]. These developments led to the formulation of what has been called dialogical pluralism [3, 1]. But in recent years this philosophical stance has received less attention, as the focus has shifted on other topics related to constructive approaches. The main topic of the talk is to present and discuss a reformulation, as well as a new start, for dialogical pluralism. The discussion will start with a presentation of the general features of the dialogical framework and how they are involved in this particular kind of pluralism. In particular we will be interested in how these features are involved in the study of non-classical logics. Some elements on the scope and limits of dialogical pluralism will also be discussed. [1] Laurent Keiff. Le Pluralisme Dialogique, PhD. Thesis, University of Lille (France), 2007. [2] Laurent Keiff, Dialogical logic, Stanford Encyclopedia of Philosophy, on- line, 2009 (accessed June 2019). [3] Shahid Rahman and Laurent Keiff, On how to be a dialogician, Logic, Thought and Action (Daniel Vanderveken, editor), Springer, Dordrecht, 2005, pp. 359{408. 3 I EDUARDO ALEJANDRO BARRIO, Substructural logics and matainferences. IIF-SADAF-CONICET, University of Buenos Aires. E-mail: [email protected]. Since the Tarskian paradigm became the standard to characterize what a logical system is, there have been different attempts to generalize it appropriately. Multiple- conclusions, non-contractive, non-monotonic, non-reflexive and even non-transitive ac- counts of what a consequence relation might be, are only some of the directions in which these investigations have been headed. In this talk I discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical sys- tems in jeopardy. In order to do this, I highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences|and more. I call to this type of entailment a meta-inference. I discuss appropriate refine- ments or modifications of the usual Tarskian identity criterion for logical systems, and propose an alternative of our own. Further, I propose to focus on a meta-inferential version of Explosion, i.e. which is concerned with inferences. In doing so, I will offer a new characterization of paraconsistency by means of which a logic is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. After that, I consider a number of objections to our account and evaluate a substantially different approach to the same problem. [1] Barrio, E., Rosenblatt, Tajer, D., The Logics of Strict-Tolerant Logic, Journal of Philosophical Logic (2015) DOI 10.1007/s10992-014-9342-6. [2] Barrio, E., Pailos, F. Szmuc, D., A Hierarchy of Classical and Paraconsistent Logics, Journal of Philosophical Logic (2019) https://doi.org/10.1007/s10992-019- 09513-z 4 CONTRIBUTED TALKS 5 I LUIS FELIPE BARTOLO ALEGRE, On falsifying empirical contradictions. Facultad de Letras y Ciencias Humanas, Universidad Nacional Mayor de San Marcos. Address: Ciudad Universtaria, Cercado de Lima, Lima, Per´u. CP: 15081. E-mail: [email protected]. The possibility of testing contradictory statements about the factual world has been suggested but barely discussed in the relevant literature. In what seems to be the only paper on the subject, Priest proposes that \if a theory entails β ^ :β, where β is some observation statement, then if such a contradiction is not observed, the theory cannot be correct" ([1]: p. 125). This presupposes that it is possible to falsify contradictory observation statements. The method proposed, though, is not adequate. In normal scientific practice, theories and other statements are falsified because of negative empirical evidence and not just for lack of positive empirical evidence, as implied by Priest's proposal. In this lecture I argue that although it may be possible to empirically verify contradictory observation sentences, it is logically impossible to empirically falsify them in any relevant way. If my argument is correct, the extension of the dialetheist programme into empirical science is, thus, non advisable since we want to avoid statements that are logically impossible to falsify. [1] Priest, Graham, Inconsistency and the Empirical Sciences, Inconsistency in Science (Meheus, Joke, editor), Springer, Dordrecht, 2002, pp. 119{28. 6 I PEDRO ZAMBRANO AND LEONARDO CANO, A natural semantics for the pull- back of fiber bundles of structures. Departamento de Matem´aticas,Universidad Nacional de Colombia, AK30 45-03 111321 Bogota, Colombia. E-mail: [email protected]. E-mail: [email protected]. Sheaves of structures on topological spaces correspond to the semantics of Intuition- ism (see [Cai95]), located in between of Kripke semantics and topoi logic. This is a paradigm of truth continuity (continuidad veritativa, according to [Cai95]), which means that if a statement is true in a point therefore it continues being true in a neighborhood of that point. There are other similar approaches of sheaves of structures in several logics (e.g., Continuous Logic -[OV16]-), where the key idea is still preserving the truth of statements in a neighborhood of a point. This idea was generalized to sheaves based on some special kind of lattices extending the lattice of open-sets of a topology (e.g., locales and quantales, [Joh02, BvdB86]), which still keeps some geometry behind them and correspond to variants of intuitionism and links topoi and quantum logic. We intend to extend this idea to fiber bundles. The pullback does not behave well with respect to forcing. Given that the pullback of a fiber bundle is a natural geomet- ric operation, a natural question is to find a semantics which is compatible with it. To do this, we use connections on fiber bundles to define the notion of parallel semantics. We find out that parallel semantics is a compatible semantics with the pullback of fiber bundles. In this semantics, the continuity of the truth is defined via curves that play the role of observers moving in space (spacetime). Parallel semantics allows to distinguish three new aspects associated to truth conti- nuity: space-time stability (truth continuity a` la Caicedo), preservation of truth of statements through the observer movement in space-time (during a time interval) and stability of the experimental measure made by the observer. [1] F. Borceux and G. van-den Bossche. Quantales and their sheaves. Order, 84C:288-301, 2017. [2] X. Caicedo. Lo?gica de los haces de estructuras. Rev. Acad. Colomb. Cienc, 19 (74):569586, 1995. [3] L. A. Cano and P. Zambrano. A natural semantics for the pullback of fiber bundles of structures. preprint. arXiv:1811.11271. Submitted. [4] P. T. Johnstone. Sketches of an elephant:
Load more

Recommended publications
  • Frontiers of Conditional Logic
    City University of New York (CUNY) CUNY Academic Works All Dissertations, Theses, and Capstone Projects Dissertations, Theses, and Capstone Projects 2-2019 Frontiers of Conditional Logic Yale Weiss The Graduate Center, City University of New York How does access to this work benefit ou?y Let us know! More information about this work at: https://academicworks.cuny.edu/gc_etds/2964 Discover additional works at: https://academicworks.cuny.edu This work is made publicly available by the City University of New York (CUNY). Contact: [email protected] Frontiers of Conditional Logic by Yale Weiss A dissertation submitted to the Graduate Faculty in Philosophy in partial fulfillment of the requirements for the degree of Doctor of Philosophy, The City University of New York 2019 ii c 2018 Yale Weiss All Rights Reserved iii This manuscript has been read and accepted by the Graduate Faculty in Philosophy in satisfaction of the dissertation requirement for the degree of Doctor of Philosophy. Professor Gary Ostertag Date Chair of Examining Committee Professor Nickolas Pappas Date Executive Officer Professor Graham Priest Professor Melvin Fitting Professor Edwin Mares Professor Gary Ostertag Supervisory Committee The City University of New York iv Abstract Frontiers of Conditional Logic by Yale Weiss Adviser: Professor Graham Priest Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional|especially counterfactual|expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that cat- alyzed the rapid maturation of the field.
    [Show full text]
  • Non-Classical Logics; 2
    {A} An example of logical metatheory would be giving a proof, Preliminaries in English, that a certain logical system is sound and com- plete, i.e., that every inference its deductive system allows is valid according to its semantics, and vice versa. Since the proof is about a logical system, the proof is not given A.1 Some Vocabulary within that logical system, but within the metalanguage. An object language is a language under discussion or be- Though it is not our main emphasis, we will be doing a fair ing studied (the “object” of our study). amount of logical metatheory in this course. Our metalan- guage will be English, and to avoid confusion, we will use A metalanguage is the language used when discussing an English words like “if”, “and” and “not” rather than their object language. corresponding object language equivalents when work- In logic courses we often use English as a metalanguage ing in the metalanguage. We will, however, be employing when discussing an object language consisting of logical a smattering of symbols in the metalanguage, including symbols along with variables, constants and/or proposi- generic mathematical symbols, symbols from set theory, tional parameters. and some specialized symbols such as “” and “ ”. ` As logical studies become more advanced and sophisti- cated, it becomes more and more important to keep the A.2 Basic Set Theory object language and metalanguage clearly separated. A logical system, or a “logic” for short, typically consists of We shall use these signs metalanguage only. (In another three things (but may consist of only the rst two, or the logic course, you might nd such signs used in the object rst and third): language.) 1.
    [Show full text]
  • Reflecting on the Legacy of CI Lewis
    Organon F, Volume 26, 2019, Issue 3 Special Issue Reflecting on the Legacy of C.I. Lewis: Contemporary and Historical Perspectives on Modal Logic Matteo Pascucci and Adam Tamas Tuboly Guest Editors Contents Matteo Pascucci and Adam Tamas Tuboly: Preface ................................... 318 Research Articles Max Cresswell: Modal Logic before Kripke .................................................. 323 Lloyd Humberstone: Semantics without Toil? Brady and Rush Meet Halldén .................................................................................................. 340 Edwin Mares and Francesco Paoli: C. I. Lewis, E. J. Nelson, and the Modern Origins of Connexive Logic ............................................... 405 Claudio Pizzi: Alternative Axiomatizations of the Conditional System VC ............................................................................................ 427 Thomas Atkinson, Daniel Hill and Stephen McLeod: On a Supposed Puzzle Concerning Modality and Existence .......................................... 446 David B. Martens: Wiredu contra Lewis on the Right Modal Logic ............. 474 Genoveva Martí and José Martínez-Fernández: On ‘actually’ and ‘dthat’: Truth-conditional Differences in Possible Worlds Semantics ............... 491 Daniel Rönnedal: Semantic Tableau Versions of Some Normal Modal Systems with Propositional Quantifiers ................................................ 505 Report Martin Vacek: Modal Metaphysics: Issues on the (Im)possible VII ............. 537 Organon F 26 (3) 2019: 318–322
    [Show full text]
  • De Finettian Logics of Indicative Conditionals
    De Finettian Logics of Indicative Conditionals Part I: Trivalent Semantics and Validity Paul Égré, Lorenzo Rossi, Jan Sprenger Abstract This paper explores trivalent truth conditions for indicative conditionals, examin- ing the “defective” table put forward by de Finetti (1936), as well as Reichenbach (1944), first sketched in Reichenbach (1935). On their approach, a conditional takes the value of its consequent whenever its antecedent is True, and the value Indeterminate otherwise. Here we deal with the problem of choosing an ade- quate notion of validity for this conditional. We show that all standard trivalent schemes are problematic, and highlight two ways out of the predicament: one pairs de Finetti’s conditional (DF) with validity as the preservation of non-False values (TT-validity), but at the expense of Modus Ponens; the other modifies de Finetti’s table to restore Modus Ponens. In Part I of this paper, we present both alternatives, with specific attention to a variant of de Finetti’s table (CC) proposed by Cooper (1968) and Cantwell (2008). In Part II, we give an in-depth treatment of the proof theory of the resulting logics, DF/TT and CC/TT: both are connexive logics, but with significantly different algebraic properties. 1 Introduction Choosing a semantics for the indicative conditional of natural language “if A, then C” (henceforth, A → C) usually involves substantial tradeoffs. The most venera- ble account identifies the indicative conditional with the material conditional ¬A ∨ C and has several attractive features: it is truth-functional, allows for a straightforward treatment of nested conditionals, and satisfies various intuitive principles such as Con- ditional Proof and Import-Export.
    [Show full text]
  • J. Michael Dunn and Greg Restall
    J. MICHAEL DUNN AND GREG RESTALL RELEVANCE LOGIC 1 INTRODUCTION 1.1 Delimiting the topic The title of this piece is not `A Survey of Relevance Logic'. Such a project was impossible in the mid 1980s when the first version of this article was published, due to the development of the field and even the space limitations of the Handbook. The situation is if anything, more difficult now. For example Anderson and Belnap and Dunn's two volume [1975, 1992] work Entailment: The Logic of Relevance and Necessity, runs to over 1200 pages, and is their summary of just some of the work done by them and their co- workers up to about the late 1980s. Further, the comprehensive bibliography (prepared by R. G. Wolf) contains over 3000 entries in work on relevance logic and related fields. So, we need some way of delimiting our topic. To be honest the fact that we are writing this is already a kind of delimitation. It is natural that you shall find emphasised here the work that we happen to know best. But still rationality demands a less subjective rationale, and so we will proceed as follows. Anderson [1963] set forth some open problems for his and Belnap's sys- tem E that have given shape to much of the subsequent research in relevance logic (even much of the earlier work can be seen as related to these open problems, e.g. by giving rise to them). Anderson picks three of these prob- lems as major: (1) the admissibility of Ackermann's rule γ (the reader should not worry that he is expected to already know what this means), (2) the decision problems, (3) the providing of a semantics.
    [Show full text]
  • CONNEXIVE CONDITIONAL LOGIC. Part I
    Logic and Logical Philosophy Volume 28 (2019), 567–610 DOI: 10.12775/LLP.2018.018 Heinrich Wansing Matthias Unterhuber CONNEXIVE CONDITIONAL LOGIC. Part I Abstract. In this paper, first some propositional conditional logics based on Belnap and Dunn’s useful four-valued logic of first-degree entailment are introduced semantically, which are then turned into systems of weakly and unrestrictedly connexive conditional logic. The general frame semantics for these logics makes use of a set of allowable (or admissible) extension/anti- extension pairs. Next, sound and complete tableau calculi for these logics are presented. Moreover, an expansion of the basic conditional connexive logics by a constructive implication is considered, which gives an oppor- tunity to discuss recent related work, motivated by the combination of indicative and counterfactual conditionals. Tableau calculi for the basic constructive connexive conditional logics are defined and shown to be sound and complete with respect to their semantics. This semantics has to ensure a persistence property with respect to the preorder that is used to interpret the constructive implication. Keywords: conditional logic; connexive logic; paraconsistent logic; Chellas frames; Segerberg frames; general frames; first-degree entailment logic; Aris- totle’s theses; Boethius’ theses; extension/anti-extension pairs; tableaux 1. Introduction In this paper we consider a weak conditional, , that satisfies un- restrictedly Aristotle’s Theses and Boethius’ Theses if a very natural condition is imposed on
    [Show full text]
  • A Truthmaker Semantics for Wansing's C
    Bachelor thesis Bsc Artificial Intelligence A Truthmaker Semantics for Wansing's C Author: Supervisor: Wouter Vromen Dr. Johannes Korbmacher Student number: Second reader: 4270630 Dr. Erik Stei A 7.5 ECTS thesis submitted in partial fulfillment of the requirements for the degree of Bachelor of Science in the Faculty of Humanities August 2020 Introduction The aim of this thesis is to provide a truthmaker semantics for the propositional connexive logic C introduced by Heinrich Wansing [28]. The basic idea of thruthmaker semantics is that the truth of propositions are necessitated by states that are wholly relevant to the truth of said propositions. Note that this "state" can be a state of affairs, a state of facts, or anything else, as long as there is a mereology which is defined in chapter 2. An overview of truthmaker semantics can be found in [12]. There are many results achieved for truthmaker semantics in the past few years; a few are highlighted here: • There is a truthmaker semantics for first degree entailment which is es- sentially due to Bas van Fraassen [15]. Kit Fine in [10] established a modernized version of this result. • Fine also defined a truthmaker semantics for full intuitionistic logic [9]. • Mark Jago did the same for relevant logic [16]. Truthmaker semantics is a new shared semantic underpinning for these logics and constructing a truthmaker semantics for Wansing's C provides a way to compare it to the rest of these logics. C is a promising four-valued semantics for connexive logic. Logic is fundamental for artificial intelligence and database reasoning.
    [Show full text]
  • Contributed Talk Abstracts1
    CONTRIBUTED TALK ABSTRACTS1 I M.A. NAIT ABDALLAH, On an application of Curry-Howard correspondence to quantum mechanics. Dep. Computer Science, UWO, London, Canada; INRIA, Rocquencourt, France. E-mail: [email protected]. We present an application of Curry-Howard correspondence to the formalization of physical processes in quantum mechanics. Quantum mechanics' assignment of complex amplitudes to events and its use of superposition rules are puzzling from a logical point of view. We provide a Curry-Howard isomorphism based logical analysis of the photon interference problem [1], and develop an account in that framework. This analysis uses the logic of partial information [2] and requires, in addition to the resolution of systems of algebraic constraints over sets of λ-terms, the introduction of a new type of λ-terms, called phase λ-terms. The numerical interpretation of the λ-terms thus calculated matches the expected results from a quantum mechanics point of view, illustrating the adequacy of our account, and thus contributing to bridging the gap between constructive logic and quantum mechanics. The application of this approach to a photon traversing a Mach-Zehnder interferometer [1], which is formalized by context Γ = fx : s; hP ; πi : s ! a? ! a; Q : s ! b? ! b; hJ; πi : a ! a0; hJ 0; πi : b ! b0; hP 0; πi : b0 ! c? ! c; Q0 : b0 ! d? ! d; P 00 : a0 ! d0? ! d0;Q00 : a0 ! c0? ! c0;R : c _ c0 ! C; S : 0 ? ? 0 ? 0 ? 00 0? 00 0? d _ d ! D; ξ1 : a ; ξ2 : b ; ξ1 : c ; ξ2 : d ; ξ1 : d ; ξ2 : c g, yields inhabitation claims: 00 00 0 0 0 R(in1(Q (J(P xξ1))ξ2 )) + R(in2(P (J (Qxξ2))ξ1)) : C 00 00 0 0 0 S(in1(P (J(P xξ1))ξ1 )) + hS(in2(Q (J (Qxξ2))ξ2)); πi : D which are the symbolic counterpart of the probability amplitudes used in the standard quantum mechanics formalization of the interferometer, with constructive (resp.
    [Show full text]
  • Humble Connexivity
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Universität München: Elektronischen Publikationen Logic and Logical Philosophy Volume 28 (2019), 513–536 DOI: 10.12775/LLP.2019.001 Andreas Kapsner HUMBLE CONNEXIVITY Abstract. In this paper, I review the motivation of connexive and strongly connexive logics, and I investigate the question why it is so hard to achieve those properties in a logic with a well motivated semantic theory. My answer is that strong connexivity, and even just weak connexivity, is too stringent a requirement. I introduce the notion of humble connexivity, which in essence is the idea to restrict the connexive requirements to possible antecedents. I show that this restriction can be well motivated, while it still leaves us with a set of requirements that are far from trivial. In fact, formalizing the idea of humble connexivity is not as straightforward as one might expect, and I offer three different proposals. I examine some well known logics to determine whether they are humbly connexive or not, and I end with a more wide-focused view on the logical landscape seen through the lens of humble connexivity. Keywords: connexive logic; strong connexivity; unsatisfiability; paraconsis- tency; conditional logic; modal logic 1. Introduction This paper is an attempt to answer a particular challenge to the en- terprise of connexive logic. It was put to me some years ago by David Makinson.1 1 Not only is he, by giving me this challenge, responsible for the existence of this paper, he also gave a number of suggestions that were of tremendous help to me in writing this paper; section 6 in particular owes its inclusion and form to these suggestions.
    [Show full text]
  • A Defense of Trivialism
    A Defense of Trivialism Paul Douglas Kabay Submitted in total fulfillment of the requirements of the degree of Doctor of Philosophy August 2008 School of Philosophy, Anthropology, and Social Inquiry The University of Melbourne Abstract That trivialism ought to be rejected is almost universally held. I argue that the rejection of trivialism should be held in suspicion and that there are good reasons for thinking that trivialism is true. After outlining in chapter 1 the place of trivialism in the history of philosophy, I begin in chapter 2 an outline and defense of the various arguments in favor of the truth of trivialism. I defend four such arguments: an argument from the Curry Paradox; and argument from the Characterization Principle; an argument from the Principle of Sufficient Reason; and an argument from the truth of possibilism. In chapter 3 I build a case for thinking that the denial of trivialism is impossible. I begin by arguing that the denial of some view is the assertion of an alternative view. I show that there is no such view as the alternative to trivialism and so the denial of trivialism is impossible. I then examine an alternative view of the nature of denial – that denial is not reducible to an assertion but is a sui generis speech act. It follows given such an account of denial that the denial of trivialism is possible. I respond to this in two ways. First, I give reason for thinking that this is not a plausible account of denial. Secondly, I show that even if it is successful, the denial of trivialism is still unassertable, unbelievable, and severely limited in its rationality.
    [Show full text]
  • Digest 2020.08.05.02.Pdf © Copyright 2020 by Colin James III All Rights Reserved
    Digest 2020.08.05.02.pdf © Copyright 2020 by Colin James III All rights reserved. ========== DMCA TAKEDOWN NOTICE ========== Attn: Copyright Agent, Scientific God Inc. (SGI), dba Huping Hu, Ph.D., J.D., [email protected]; dba Maoxin Wu, M.D., Ph.D., [email protected] Owner of: [Domain scigod.com IP: 45.33.14.160 Registrar: [email protected]; Hosting: [email protected]] [Domain vixra.org IP: 192.254.236.78 Registrar: [email protected]; Hosting: [email protected]] [Domain rxiv.org IP: 162.241.226.73 Registrar: [email protected]; Hosting: [email protected]] [Domain s3vp.vixrapedia.org IP: 2a01:4f8:c2c:58fa::1 = 116.203.89.52 Registrar: [email protected]; Hosting: [email protected]] Pursuant to 17 USC 512(c)(3)(A), this communication serves as a statement that: I am the exclusive rights holder for at least 716 articles of duly copyrighted material being infringed upon listed at these URLs https://vixra.org/author/colin_james_iii https://rxiv.org/author/colin_james_iii ; and any other as yet undiscovered locations operated by SGI or dba as Phil Gibbs of UK. These exclusive rights are being violated by material available upon your site at the following URL(s): See the attached list of URLs of infringing material herewith as Exhibit 5 and Exhibit 6; I have a good faith belief that the use of this material in such a fashion is not authorized by the copyright holder or the law; Under penalty of perjury in United States District Court, I state that the information contained in this notification is accurate, and that I am authorized to act as the exclusive rights holder for the material in question; I may be contacted by the following methods: Colin James III, 405 E Saint Elmo Ave Apt 204, Colorado Springs, CO 80905; [email protected]; (719) 210-9534.
    [Show full text]
  • Kripke Completeness of Bi-Intuitionistic Multilattice Logic and Its Connexive Variant
    Norihiro Kamide Kripke Completeness of Yaroslav Shramko Bi-intuitionistic Multilattice Heinrich Wansing Logic and its Connexive Variant Abstract. In this paper, bi-intuitionistic multilattice logic, which is a combination of multilattice logic and the bi-intuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzen-type sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into bi-intuitionistic logic. The logic proposed is an extension of first-degree entailment logic and can be regarded as a bi-intuitionistic variant of the original classical multilattice logic determined by the algebraic structure of multilattices. Similar completeness and embedding results are also shown for another logic called bi- intuitionistic connexive multilattice logic, obtained by replacing the connectives of intu- itionistic implication and co-implication with their connexive variants. Keywords: First-degree entailment logic, Multilattices, Bi-intuitionistic logic, Connexive logic. Introduction The aim of this paper is to expand the realm of the first-degree entailment logic (FDE) first presented by Anderson and Belnap [2,3,5], and justified semantically by Dunn [9] and Belnap [7,8]. FDE, also called Belnap and Dunn’s four-valued logic, is widely considered to be very useful for a number of different purposes in philosophy and computer science. This logic is based on a compound algebraic structure known as a bilattice [10–12] and allows various natural generalizations that can be pursued along different lines. One such line leads to the notion of a trilattice [32] and—more generally— multilattice, resulting in logical systems comprising more than one con- sequence relation, notably bi-consequence systems [25,26,33] and multi- consequence systems [31].
    [Show full text]