scholarly journals Power Matrices and Dunn--Belnap Semantics: Reflections on a Remark of Graham Priest

2014 ◽  
Vol 11 (1) ◽  
Author(s):  
Lloyd Humberstone
Keyword(s):  
Equational Logic ◽  
Consequence Relations ◽  
Consequence Relation ◽  
Power Matrix ◽  
Matrix Construction ◽  
The Given ◽  
The Universe ◽  
Power Algebras ◽  
Graham Priest ◽  
Natural Way

The plurivalent logics considered in Graham Priest's recent paper of that name can be thought of as logics determined by matrices (in the `logical matrix' sense) whose underlying algebras are power algebras (a.k.a. complex algebras, or `globals'), where the power algebra of a given algebra has as elements \textit{subsets} of the universe of the given algebra, and the power matrix of a given matrix has has the power algebra of the latter's algebra as its underlying algebra, with its designated elements being selected in a natural way on the basis of those of the given matrix. The present discussion stresses the continuity of Priest's work on the question of which matrices determine consequence relations (for propositional logics) which remain unaffected on passage to the consequence relation determined by the power matrix of the given matrix with the corresponding (long-settled) question in equational logic as to which identities holding in an algebra continue to hold in its power algebra. Both questions are sensitive to a decision as to whether or not to include the empty set as an element of the power algebra, and our main focus will be on the contrast, when it is included, between the power matrix semantics (derived from the two-element Boolean matrix) and the four-valued Dunn--Belnap semantics for first-degree entailment a la Anderson and Belnap) in terms of sets of classical values (subsets of {T, F}, that is), in which the empty set figures in a somewhat different way, as Priest had remarked his 1984 study, `Hyper-contradictions', in which what we are calling the power matrix construction first appeared.

scholarly journals Relevance in Structured Argumentation

2018 ◽  
Author(s):  
AnneMarie Borg ◽  
Christian Straßer
Keyword(s):  
Irrelevant Information ◽  
Argumentation Theory ◽  
Relevance Logic ◽  
Consequence Relations ◽  
Consequence Relation ◽  
Relevance Criteria ◽  
Structured Argumentation ◽  
Semantic Relevance ◽  
The Given ◽  
Argumentation Systems

We study properties related to relevance in non-monotonic consequence relations obtained by systems of structured argumentation. Relevance desiderata concern the robustness of a consequence relation under the addition of irrelevant information. For an account of what (ir)relevance amounts to we use syntactic and semantic considerations. Syntactic criteria have been proposed in the domain of relevance logic and were recently used in argumentation theory under the names of non-interference and crash-resistance. The basic idea is that the conclusions of a given argumentative theory should be robust under adding information that shares no propositional variables with the original database. Some semantic relevance criteria are known from non-monotonic logic. For instance, cautious monotony states that if we obtain certain conclusions from an argumentation theory, we may expect to still obtain the same conclusions if we add some of them to the given database. In this paper we investigate properties of structured argumentation systems that warrant relevance desiderata.

Combo separability criteria and lower bound on concurrence

2021 ◽  
Author(s):  
Zangi Sultan ◽  
Jiansheng Wu ◽  
Cong-Feng Qiao
Keyword(s):  
Lower Bound ◽  
Correlation Matrix ◽  
Density Operator ◽  
Singular Values ◽  
Quantum Information Theory ◽  
Separability Criteria ◽  
The Given ◽  
Ky Fan ◽  
Natural Way ◽  
Extract Information

Abstract Detection and quantification of entanglement are extremely important in quantum information theory. We can extract information by using the spectrum or singular values of the density operator. The correlation matrix norm deals with the concept of quantum entanglement in a mathematically natural way. In this work, we use Ky Fan norm of the Bloch matrix to investigate the disentanglement of quantum states. Our separability criterion not only unifies some well-known criteria but also leads to a better lower bound on concurrence. We explain with an example how the entanglement of the given state is missed by existing criteria but can be detected by our criterion. The proposed lower bound on concurrence also has advantages over some investigated bounds.

Equational Logic Programming

1998 ◽  
Author(s):  
Michael J. O’Donnell
Keyword(s):  
Normal Form ◽  
Logic Programming ◽  
Programming Languages ◽  
Question Answering ◽  
Normal Forms ◽  
Equational Logic ◽  
Consequence Relation ◽  
Logic Programming Languages ◽  
Semantic Consequence

Sections 2.3.4 and 2.3.5 of the chapter ‘Introduction: Logic and Logic Programming Languages’ are crucial prerequisites to this chapter. I summarize their relevance below, but do not repeat their content. Logic programming languages in general are those that compute by deriving semantic consequences of given formulae in order to answer questions. In equational logic programming languages, the formulae are all equations expressing postulated properties of certain functions, and the questions ask for equivalent normal forms for given terms. Section 2.3.4 of the ‘Introduction . . .’ chapter gives definitions of the models of equational logic, the semantic consequence relation . . . T |=≐(t1 ≐ t2) . . . (t1 ≐ t2 is a semantic consequence of the set T of equations, see Definition 2.3.14), and the question answering relation . . . (norm t1,…,ti : t) ?- ≐ (t ≐ s) . . . (t ≐ s asserts the equality of t to the normal form s, which contains no instances of t1, . . . , ti, see Definition 2.3.16).

What Would a Phenomenology of Logic Look Like?

Mind ◽  
2019 ◽  
Vol 129 (516) ◽  
pp. 1009-1031
Author(s):  
James Kinkaid
Keyword(s):  
Logical Consequence ◽  
Philosophy Of Logic ◽  
Contemporary Philosophy ◽  
Consequence Relations ◽  
Consequence Relation ◽  
If Logic ◽  
Pure Logic ◽  
Logical Investigations ◽  
Normative Status ◽  
Selection Of

Abstract The phenomenological movement begins in the Prolegomena to Husserl’s Logical Investigations as a philosophy of logic. Despite this, remarkably little attention has been paid to Husserl’s arguments in the Prolegomena in the contemporary philosophy of logic. In particular, the literature spawned by Gilbert Harman’s work on the normative status of logic is almost silent on Husserl’s contribution to this topic. I begin by raising a worry for Husserl’s conception of ‘pure logic’ similar to Harman’s challenge to explain the connection between logic and reasoning. If logic is the study of the forms of all possible theories, it will include the study of many logical consequence relations; by what criteria, then, should we select one (or a distinguished few) consequence relation(s) as correct? I consider how Husserl might respond to this worry by looking to his late account of the ‘genealogy of logic’ in connection with Gurwitsch’s claim that ‘[i]t is to prepredicative perceptual experience … that one must return for a radical clarification and for the definitive justification of logic’. Drawing also on Sartre and Heidegger, I consider how prepredicative experience might constrain or guide our selection of a logical consequence relation and our understanding of connectives like implication and negation.

Das Präphysiche Stadium und der Anfang der Welt

1998 ◽  
pp. 74-80
Author(s):  
Malgorzata Szczesniak
Keyword(s):  
Physical State ◽  
Big Bang ◽  
Evolution Of The Universe ◽  
Time Period ◽  
The Creation ◽  
The Absolute ◽  
The Big Bang ◽  
The Universe ◽  
Natural Way

This paper concerns the main physical, philosophical and existential aspects of the ‘pre-physical’ stage in the evolution of the universe. I will discuss the ways that contemporary cosmology tries to: (1) solve the problem about the time period of the ‘pre-physical’ state; (2) answer the question whether the beginning of time was at the same time as the beginning of the existence of the Universe; (3) answer another whether the Big Bang was an absolute beginning of the existence of the Universe or only a beginning of some stage of its evolution; (4) respond to another question whether the absolute beginning of the Universe inevitably implies its creation by God or whether it allows for the possibility of the creation of the Universe in a natural way; and (5) discuss the issue of the ‘singular’ moment. All of these questions, in particular the last one, will be discussed with reference to the latest achievements in the fields of physics and cosmology.

scholarly journals Extending trinity to the scalar sector through discrete flavoured symmetries

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
João M. Alves ◽  
Francisco J. Botella ◽  
Gustavo C. Branco ◽  
Miguel Nebot
Keyword(s):  
Mass Matrix ◽  
Baryon Asymmetry ◽  
Tree Level ◽  
Strong Reduction ◽  
Ckm Matrix ◽  
The Standard Model ◽  
The Universe ◽  
The Trinity ◽  
Scalar Sector ◽  
Natural Way

Abstract We conjecture the existence of a relation between elementary scalars and fermions, making it plausible the existence of three Higgs doublets. We introduce a Trinity Principle (TP) which, given the fact that there are no massless quarks, requires the existence of a minimum of three Higgs doublets. The TP states that each row of the mass matrix of a quark of a given charge should receive the contribution from one and only one scalar doublet and furthermore a given scalar doublet should contribute to one and only one row of the mass matrix of a quark of a given charge. This principle is analogous to the Natural Flavour Conservation (NFC) of Glashow and Weinberg with the key distinction that NFC required the introduction of a flavour blind symmetry, while the TP requires a flavoured symmetry, to be implemented in a natural way. We provide two examples which satisfy the Trinity Principle based on $${\mathbb {Z}}_3$$Z3 and $${\mathbb {Z}}_2\times {\mathbb {Z}}_2'$$Z2×Z2′ flavoured symmetries, and show that they are the minimal multi-Higgs extensions of the Standard Model where CP can be imposed as a symmetry of the full Lagrangian and broken by the vacuum, without requiring soft-breaking terms. We show that the vacuum phases are sufficient to generate a complex CKM matrix, in agreement with experiment. The above mentioned flavoured symmetries lead to a strong reduction in the number of parameters in the Yukawa interactions, enabling a control of the Scalar Flavour Changing Neutral Couplings (SFCNC). We analyse some of the other physical implications of the two models, including an estimate of the enhancement of the Baryon Asymmetry of the Universe provided by the new sources of CP violation, and a discussion of the strength of their tree-level SFCNC.

QUANTUM CORRECTIONS HELP EINSTEIN GRAVITY EXIT GRACIOUSLY

1991 ◽  
Vol 06 (10) ◽  
pp. 861-867 ◽  
Author(s):  
J. PÉREZ-MERCADER
Keyword(s):  
Initial Period ◽  
Einstein Gravity ◽  
Bubble Nucleation ◽  
Time Dependent ◽  
Quantum Corrections ◽  
Exponential Potential ◽  
Exit Problem ◽  
Conformal Equivalence ◽  
The Universe ◽  
Natural Way

We exploit the conformal equivalence between the 1-loop corrected Einstein gravity coupled to a scalar field, and linear Einstein gravity with an exponential potential, to show how the Graceful Exit Problem is solved in the context of this theory in a natural and simple way. What emerges is a scenario with a chaotic initial period followed by an era of old inflation. The resulting bubble nucleation rate is time-dependent in such a way that the second inflationary period, helped by the chaotic period, brings the Universe out of its inflationary era in a self-regulated and natural way.

scholarly journals LINGUOCULTURE AND LINGUOCULTUREME

2019 ◽  
Vol 3 (4) ◽  
pp. 111-114
Author(s):  
Malokhat Muhammadovna Juraeva ◽  
◽  
Muborak Khafizovna Khamidova
Keyword(s):  
The Given ◽  
The Universe

In the given article, language is interpreted not only as a means for expressing thoughts, but also as a product of thinking and an integral part of the whole world and the universe, as an important part of culture. Also, such terms as 'linguoculturology 'and' linguocultureme' are also widely disscussed

scholarly journals Linguistic formulas - a priority of modern teaching "In the universe of grammar I"

2021 ◽  
Vol X (3) ◽  
pp. 147-151
Author(s):  
Nana Shavtvaladze ◽  
Keyword(s):  
Second Language ◽  
Foreign Language ◽  
21St Century ◽  
Online Teaching ◽  
English Language ◽  
The Common ◽  
A Priority ◽  
The Given ◽  
The Universe

We have the variety of forms, ways, methods, strategies of teaching in the 21st century. It`s important to achieve the goal, to gain the result, to perceive the given materials. Everyone is free to choose any ways from the given approaches. Most of the textbooks are dedicated to English language. English is dominated worldwide and it`s not only foreign language but a second language as well in many countries. There are different visions and approaches in teaching a language as a foreign or as a second one. Textbooks are mades based on the four skills: reading, writing, speaking, listening. Demand of Georgian as a foreign language has increased. Many philologists have occupied themselves with teaching Georgian as a Foreign language. Plus, they have means of teaching, once there are many textbooks already created, especially for the beginner levels. Online teaching has also increased these demands. Every author forms his/her own style, approach and vision when creating a textbook. In my opinion, it`s important to first calculate the common methodical view from the beginning to the end and only then start working on the new textbook. This kind of approach helps instructor gain the results and consistent logical motion is encouraging hopeful for the student.

A Variety of Causes

2020 ◽  
Author(s):  
Paul Noordhof
Keyword(s):  
Fundamental Property ◽  
Causal Chain ◽  
The Other ◽  
Counterfactual Analysis ◽  
Humean Supervenience ◽  
Transitive Relation ◽  
Fundamental Type ◽  
The Difference ◽  
The Universe ◽  
Natural Way

Metaphysicians often focus on what is vertically fundamental, appealing to grounding or truth-making, rather than what is horizontally fundamental: what must be common to any metaphysical picture of the universe. There is a case for causation being one such feature. But how should it be characterized? A revised semantics for counterfactuals provides the basis for a new counterfactual analysis of causation that is compatible with Humean supervenience but also appropriate for a non-Humean metaphysical framework. Causes (independently of their competitors) both make the chance of an effect very much greater than its mean background chance in the circumstances and actually influences the probability of the effect in this way at the time at which the effect occurred via a complete causal chain. Causation understood in this way is a non-transitive relation. It is neutral over the metaphysics of causes and effects but allows a natural way for events to be understood as one fundamental type of causation, the other being property causation. Although negative causal statements are true, there are no cases of negative causation. The analysis explains how causation involving substantial processes is only one variety of causation, others include double prevention. It allows for a variety of micro- and macro-properties to be the basis of the difference between cause and effect. Laws are patterns of causation realized in different ways in different metaphysical pictures. The analysis of causation characterizes a horizontally fundamental property whose modal character depends upon its different realizations.

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