In this paper we study the systems P and $P^{\ast}$ (see Arruda and da Costa, O paradoxo de Curry-Moh Shaw-Kwei, Boletim da Sociedade Matemātica de São Paulo 18 (1966)) and some related systems. In the last section, we prove that certain set theories having P and $P^{\ast}$ as their underlying logics are non-trivial.

The tableaux-constructions have a number of properties which advantageously distinguish them from equivalent axiomatic systems . The proofs in the form of tableaux-constructions have a full accordance with semantic interpretation and subformula property in the sense of Gentzen’s Hauptsatz. Method of tatleaux-construction gives a good substitute of Gentzen’s methods and thus opens a good perspective for the investigations of theoretical as well as applied aspects of logical calculi. It should be noted that application of tableau method in modal, tense, relevant (...) and other non-classical logics is connected with serious difficulties. Tableaux variants are constructed only for a few normal modal systems. As to relevant and paraconsistent logic, the absence of its tableau variants may be considered as a question of special interest. We shall formulate the tableaux for propositional modal system S4.1, S4.2, S4.3, S4.4 and relevant R∗ and E ∗ using Beth’s tableaux construction with indexed formulas. (shrink)

EI objetivo de este artículo es presentar los principios de la programación lógica borrosa y de sus principales variantes, ilustrándolas a través de un conjunto de aproximaciones que, a nuestro entender, son representativas de los avances en esta área. También incluimos la descripción de otros sistemas de programación lógica que se sustentan en lógicas de la incertidumbre diferentes de la lógica borrosa. En esta presentación presuponemos que la mayoría de los lectores no son expertos en programación lógica; para seguirla sólo (...) se requiere un conocimiento básico de la lógica de predicados.The purpose of this paper is to present the principles of the fuzzy logic programming, exemplifying them by a couple of proposals that we think are representatives of the advances in this field. We include also the description of another systems of logic programming with uncertain information that are based on other logics of uncertainty which are different from fuzzy logic. This article only presuppose anelementary knowledge of the classical first-order logic. (shrink)

The aim of this paper is to present a modified version of the notion of strong proof from hypotheses (definition D2), and to give three deduction theorems for the relevant logicsR (theoremsT1, andT2) andE (theoremT3).

The system R, or more precisely the pure implicational fragment R›, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance logic is RM or R-mingle. The question is whether adding mingle axiom to R› yields the pure implicational fragment RM› of the system? As concerns the (...) weak systems there are at least two approaches to the problem. First of all, it is possible to restrict a validity of some theorems. In another approach we can investigate even weaker logics which have no theorems and are characterized only by rules of deducibility. (shrink)

This paper is a study of four subscripted Gentzen systems G u R +, G u T +, G u RW + and G u TW +. [16] shows that the first three are equivalent to the semilattice relevant logics u R +, u T + and u RW + and conjectures that G u TW + is, equivalent to u TW +. Here we prove Cut Theorems for these systems, and then show that modus ponens is admissible — which (...) is not so trivial as one normally expects. Finally, we give decision procedures for the contractionless systems, G u TW + and G u RW +. (shrink)

A method is presented for constructing natural deduction-style systems for propositional relevant logics. The method consists in first translating formulas of relevant logics into ternary relations, and then defining deduction rules for a corresponding logic of ternary relations. Proof systems of that form are given for various relevant logics. A class of algebras of ternary relations is introduced that provides a relation-algebraic semantics for relevant logics.

The standard Hilbert-style of axiomatic system yields the assertion of axioms and, via the use of rules, the assertion of theorems. However, there has been little work done on the corresponding axiomatic rejection of non-theorems. Such Hilbert-style rejection would be achieved by the inclusion of certain rejection-axioms (r-axioms) and, by use of rejection-rules (r-rules), the establishment of rejection-theorems (r-theorems). We will call such a proof a rejection-proof (r-proof). The ideal to aim for would be for the theorems and r-theorems (...) to bemutually exclusive and exhaustive. That is, if a formula A is a theorem then it is not an r-theorem, and if A is a non-theorem then it is an r-theorem. In this paper, I present a rejecion system for the first-degree formulae of a large number of relevant logics. (shrink)

ABSTRACTSince 2010, there have been series of discussions by stakeholders to revamp Ghana’s current juvenile justice system to make it more relevant and sustainable within Ghana’s domestic context....

We present axiomatizations of the deontic fragment of Anderson's relevant deontic logic (the logic of obligation and related concepts) and the eubouliatic fragment of Anderson's eubouliatic logic (the logic of prudence, safety, risk, and related concepts).

In this paper, the positive fragment of the logic math formula of contraction-less relevant implication is extended with the addition of a paraconsistent negation connective similar to the strong negation connective in Nelson's paraconsistent four-valued logic math formula. This extended relevant logic is called math formula, and it has the property of constructible falsity which is known to be a characteristic property of math formula. A Gentzen-type sequent calculus math formula for math formula is introduced, and the cut-elimination and decidability (...) theorems for math formula are proved. Two extended Routley-Meyer semantics are introduced for math formula, and the completeness theorems with respect to these semantics are proved. (shrink)

In this paper we study the systemsP andP * (see Arruda and da Costa,O paradoxo de Curry-Moh Shaw-Kwei, Boletim da Sociedade Matemtica de São Paulo 18 (1966)) and some related systems. In the last section, we prove that certain set theories havingP andP * as their underlying logics are non-trivial.

This paper describes the Eunomos software, an advanced legal document and knowledge management system, based on legislative XML and ontologies. We describe the challenges of legal research in an increasingly complex, multi-level and multi-lingual world and how the Eunomos software helps users cut through the information overload to get the legal information they need in an organized and structured way and keep track of the state of the relevant law on any given topic. Using NLP tools to semi-automate the (...) lower-skill tasks makes this ambitious project a realistic commercial prospect as it helps keep costs down while at the same time allowing greater coverage. We describe the core system from workflow and technical perspectives, and discuss applications of the system for various user groups. (shrink)

In this paper two deductive systems associated with relevance logic are studied from an algebraic point of view. One is defined by the familiar, Hilbert-style, formalization of R; the other one is a weak version of it, called WR, which appears as the semantic entailment of the Meyer-Routley-Fine semantics, and which has already been suggested by Wójcicki for other reasons. This weaker consequence is first defined indirectly, using R, but we prove that the first one turns out to be (...) an axiomatic extension of WR. Moreover we provide WR with a natural Gentzen calculus. It is proved that both deductive systems have the same associated class of algebras but different classes of models on these algebras. The notion of model used here is an abstract logic, that is, a closure operator on an abstract algebra; the abstract logics obtained in the case of WR are also the models, in a natural sense, of the given Gentzen calculus. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The contributors to Nervous Systems reassess contemporary artists' and critics' engagement with social, political, biological, and other systems as a set of complex and relational parts: an approach commonly known as systems thinking. Demonstrating the continuing relevance of systems aesthetics within contemporary art, the contributors highlight the ways that artists adopt systems thinking to address political, social, and ecological anxieties. They cover a wide range of artists and topics, from the performances of the Argentinian collective the Rosario Group and (...) the grid drawings of Charles Gaines to the video art of Singaporean artist Charles Lim and the mapping of global logistics infrastructures by contemporary artists like Hito Steyerl and Christoph Büchel. Together, the essays offer an expanded understanding of systems aesthetics in ways that affirm its importance beyond technological applications detached from cultural contexts. (shrink)

The nature and structure of time and time-intervals in physical, chemical and biological systems will be elucidated. The relation and dependence among time, energy and taking place of natural processes will be critically analyzed. The bio-processes taking place in nano-time intervals will be identified. Their relevance to nano-bio-science and nano-bio-technology will be developed and nano-time interval-aspect of nano-sciences and nano-technology will be advanced. -/- .

Post-Traumatic Stress Disorder is a major public health concern in both civilian and military populations, across race, age, gender, and socio-economic status. While PTSD has been around for centuries by some name or another, its definition and description also continue to evolve. Within the last few years, the American Psychological Association has published the 5th edition of the Diagnostic and Statistical Manual of Mental Disorders, which includes some major changes in the diagnostic criteria for PTSD. Recent data on epidemiology, etiological (...) theories, and empirically supported methods of treatment, as well as implications for legal processes and criminal justice system personnel, are discussed. (shrink)

The purpose of the present text is to show the importance of the system of relevances in respect of the analysis of the literary texts. This concept, developed by Alfred Schutz, helps not only to understand the relation between text and empirical reality as such, but it simultaneously questions the relation between reader, writer, and text. The questions raised by the status of the system of relevances help the phenomenological analysis of the literary text to achieve a better (...) understanding of the act of signification (particularly that defined in the realm of literature) and of the status of reference. It helps also to understand how the configuration of experience as such can be modified according to the specific interaction accomplished within the act of reading. (shrink)

Anderson and Belnap presented indexed Fitch-style natural deduction systems for the relevant logics R, E, and T. This work was extended by Brady to cover a range of relevant logics. In this paper I present indexed tree natural deduction systems for the Anderson–Belnap–Brady systems and show how to translate proofs in one format into proofs in the other, which establishes the adequacy of the tree systems.

Once upon a time, modal logic was castigated because it ‘had no semantics.’ Kripke, Hintikka, Kanger, and others changed all that. In a similar way, when Relevant Logic was introduced by Anderson and Belnap, it too was castigated for ‘having no semantics.’ The present overview marks a culmination of that effort. The semantic approach described here brings together a number of hitherto disparate efforts to set out formal systems for logics of relevant implication and entailment. It also makes clear (despite (...) some of our hopes and utterances) that the One True Logic does not exist. This is as true for relevant logics as Kripke et al., showed it to be for modal logics. In both cases, subtle (and not so subtle) variations on semantical postulates produce different logics in the same family. The question of which semantical postulates are correct makes no sense without further context, i.e., the questioner needs to answer the question: Correct for what? The question that does remain is: What motivates the relevant family of logics? And this is the question that is the main job for this chapter to investigate. (shrink)

New coverage of the recent wars in Afghanistan and Iraq, and the ensuing public education campaigns by the Department of Veterans Affairs and private veterans advocacy groups combine to call the public's attention to the many potential mental health problems associated with traumatic event exposure. Indeed, since 2001, Operation Iraqi Freedom and Operation Enduring Freedom combat and peacekeeping missions have been characterized by high levels of exposure to acts of extreme violence, with often gruesome effects. Less publically discussed is the (...) fact that a surprisingly large number of United States civilians also report exposure to traumatic events, such as severe interpersonal violence, natural disasters, and serious automobile accidents. In fact, approximately 70% of randomly sampled respondents indicated that they have experienced an incident characterized by significant perceived life threat at some point during their lives. (shrink)

Comparative research assessing metacognition in nonhuman animals contributes to the question of what form introspection could take in humans, non-humans, and other possibly conscious systems. We briefly review some major findings in comparative metacognition research, including some discoveries in areas looking at self-regulation and self-control. We discuss what data exist to address the three conditions for introspection defined by Kammerer and Frankish (this issue) in their target article. We suggest that two of three conditions are met by existing data from (...) non-human primates, and that the third condition may be more difficult, but perhaps not impossible, to assess. We argue that a comparative and developmental approach to this question of how to define and measure introspection is a productive avenue to make progress in this area. (shrink)

The paper discusses how systems biology is working toward complex accounts that integrate explanation in terms of mechanisms and explanation by mathematical models—which some philosophers have viewed as rival models of explanation. Systems biology is an integrative approach, and it strongly relies on mathematical modeling. Philosophical accounts of mechanisms capture integrative in the sense of multilevel and multifield explanations, yet accounts of mechanistic explanation have failed to address how a mathematical model could contribute to such explanations. I discuss how mathematical (...) equations can be explanatorily relevant. Several cases from systems biology are discussed to illustrate the interplay between mechanistic research and mathematical modeling, and I point to questions about qualitative phenomena, where quantitative models are still indispensable to the explanation. Systems biology shows that a broader philosophical conception of mechanisms is needed, which takes into account functional-dynamical aspects, interaction in complex networks with feedback loops, system-wide functional properties such as distributed functionality and robustness, and a mechanism’s ability to respond to perturbations. I offer general conclusions for philosophical accounts of explanation. (shrink)

This thesis seeks to extend the search for the moral implications inherent in the development, possession and threatened use of physical/astrophysical processes and in current understandings of the evolution of the physical universe. ;The nature of moral/theological discussion will not be a primary concern although clearly some residual position that such discussion is meaningful is presupposed. Neither is the nature of science or the scientific method at issue. It is assumed that both theology and science have long since negotiated the (...) confidence crises of adolescence and have mustered the requisite self-esteem regarding their respective disciplines. ;The aim of this work is to present the concept of time-scales as a relevant moral category. It will investigate the use of this concept and its relationship to the other categories developed in the relevant scientific literature. Similarly, the use of this concept will be explored and its influence sought in the analogous documentation from the Catholic tradition. In this investigation the question will be raised as to the validity of and the future of the concept of time-scales as a common moral ground for these two traditions, enhancing convergence and leading toward a more direct collaboration on the question of human survival. (shrink)

This paper discusses three relevant logics that obey Component Homogeneity - a principle that Goddard and Routley introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity - that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S*fde, dS*fde, crossS*fde. Second, the paper establishes complete sequent calculi (...) for S*fde, dS*fde, crossS*fde. Among the other accomplishments of the paper, we generalize the semantics from Bochvar, Hallden, Deutsch and Daniels, we provide a general recipe to define containment logics, we explore the single-premise/single-conclusion fragment of S*fde, dS*fde, crossS*fdeand the connections between crossS*fde and the logic Eq of equality by Epstein. Also, we present S*fde as a relevant logic of meaninglessness that follows the main philosophical tenets of Goddard and Routley, and we briefly examine three further systems that are closely related to our main logics. Finally, we discuss Routley's criticism to containment logic in light of our results, and overview some open issues. (shrink)