Nonstandard theories of quantification and identity

1970 ◽  
Vol 35 (2) ◽  
pp. 267-294 ◽  
Author(s):  
A. Trew
Keyword(s):  
Predicate Logic ◽  
Type A ◽  
The Other ◽  
Standard System ◽  
Free Logic ◽  
Quantification Theory ◽  
Singular Terms ◽  
Free Variables

In this paper a number of nonstandard systems of predicate logic with or without identity, are translated with subsystems of applied standard system of predicate logic with identity. There are nonstandard theories of quantification which, following [16], are described as inclusive systems; their theorems are valid in all domains, including the empty domain. Theories of quantification which allow for the substitution of denotationless terms for free variables, are described, following [21], as systems of free logic; they are said to be free of the requirement that all singular terms must have denotations. Free logics and inclusive logics may each be of the other type. A nonstandard theory of identity, described, following [12] as a theory of nonreflexive identity, may be combined with a standard or with a nonstandard theory of quantification. Another kind of nonstandard system of predicate logic examined is a nonstandard version of a system of monadic predicate logic in which a distinction is made between sentence and predicate negation, and which is nonstandard in the sense that the laws relating sentence and predicate negation diverge from the standard ones. In the systems examined, this is combined with an inclusive quantification theory.

Free logics, philosophical issues in

2018 ◽  
Author(s):  
Karel Lambert
Keyword(s):  
Predicate Logic ◽  
Philosophy Of Mathematics ◽  
Logical Truth ◽  
General Term ◽  
Free Logic ◽  
Singular Terms ◽  
Restricted Version ◽  
General Terms ◽  
Classical Predicate ◽  
As If

The expression ‘free logic’ is a contraction of the more cumbersome ‘logic free of existence assumptions with respect to both its general terms (predicates) and its singular terms’. Its most distinctive feature is the rejection of the principle of universal specification, a principle of classical predicate logic which licenses the logical truth of statements such as ‘If everything rotates then (the planet) Mars rotates’. If a free logic contains the general term ‘exists’, this principle is replaced by a restricted version, one which licenses the logical truth only of statements such as ‘If everything rotates then Mars rotates, provided that Mars exists’. If the free logic does not contain the general term ‘exists’, but contains the term ‘is the same as’, the principle is replaced by a version which licenses only statements such as ‘If everything rotates then Mars rotates, provided that there is an object the same as Mars’. Most free logicians regard the restricted version of universal specification as simply making explicit an implicit assumption, namely, that Mars exists. Indeed, free logic is the culmination of a long historical trend to rid logic of existence assumptions with respect to its terms. Just as classical predicate logic purports to be free of the hidden existence assumptions which pervaded the medieval theory of inference with respect to its general terms, so free logic rids classical predicate logic of hidden existence assumptions with respect to its singular terms. There are various kinds of free logic, with many interesting and novel philosophical applications. These cover a wide range of issues from the philosophy of mathematics to the philosophy of religion. In addition to the issue of how to analyse singular existence statements, of the form ‘3 + 7 exists’ and ‘That than which nothing greater can be conceived exists’, of special importance are issues in the theory of definite descriptions, set theory, the theory of reference, modal logic and the theory of complex general terms.

Anatomie, histologie et affinités de l'appareil séricigène des Hersilia Sav. et Aud. (Araneae: Hersiliidae)

1984 ◽  
Vol 62 (1) ◽  
pp. 97-106 ◽  
Author(s):  
Jacqueline Kovoor
Keyword(s):  
Type A ◽  
The Other ◽  
Secretory Cells ◽  
Evolutionary Stage ◽  
Type B ◽  
Outer Coat ◽  
Silk Glands ◽  
Single Protein

Although hersiliid spiders do not spin any webs, their silk glands, which belong to six types, are large and complex. Two groups of ampullate glands, one opening on the anterior spinnerets and the other on the median spinnerets, secrete two proteins each. About 180 pyriform glands are clearly bipartite. Over 200 type A aciniform glands opening on the median and posterior spinnerets are made up of three categories of secretory cells. Silk from these glands consists of two proteins (core and outer coat) joined together by an intermediary layer of acidic glycoprotein. All the 160 type B aciniform glands opening on the posterior spinnerets secrete a single protein. Fifty tubuliform glands opening on the median and posterior spinnerets produce two proteins, one of which is coloured. As in Urocteinae, long posterior spinnerets and large, numerous aciniform and tubuliform glands are correlated with swathing of prey and egg-cocoon construction. In Lycosidae and Agelenidae, the ampullate glands show the same number and distribution according to the spinnerets. However, anatomical and histochemical features of hersiliid aciniform and ampullate glands are close to those of some Araneoidea. Apart from peculiar characteristics, silk glands of Hersilia might represent an intermediate evolutionary stage towards Araneoidea.

The infrared spectrum of di-imide near 7.6 μm

1981 ◽  
Vol 59 (5) ◽  
pp. 663-672 ◽  
Author(s):  
K-E. J. Hallin ◽  
J. W. C. Johns ◽  
A. Trombetti
Keyword(s):  
Infrared Spectrum ◽  
Gas Phase ◽  
Type A ◽  
Phase Spectrum ◽  
The Other ◽  
Mode Analysis ◽  
Simultaneous Presence ◽  
Torsional Mode ◽  
Bending Mode ◽  
Type C

The gas phase spectrum of N2H2 has been investigated in the region of 7.6 μm at a resolution of about 0.06cm−1. Two bands have been identified; one, near 1288 cm−1, is a type C band and must correspond to ν4 (the hitherto unidentified Au torsional mode), and the other, near 1317 cm−1, is a type A–B hybrid and corresponds to ν6 (the Bu bending mode). Analysis of the spectrum is complicated by the simultaneous presence of strong A-type and B-type Coriolis interactions which couple the observed levels.

Singular Terms, Truth-Value Gaps, and Free Logic

1966 ◽  
Vol 63 (17) ◽  
pp. 481 ◽  
Author(s):  
Bas C. van Fraassen
Keyword(s):  
Free Logic ◽  
Singular Terms ◽  
Truth Value

The Problem of de re Modality

2020 ◽  
pp. 234-246
Author(s):  
Bob Hale
Keyword(s):  
Kit Fine ◽  
Singular Terms ◽  
De Re ◽  
Modal Operators ◽  
Free Variables ◽  
De Re Modality ◽  
Basic Argument ◽  
De Dicto

The problem of de re modality is how, if at all, one can make sense of it. Most who have discussed this problem have assumed that modality de dicto is relatively unproblematic. It is, rather, the interpretation of sentences involving, within the scope of modal operators, singular terms or free variables which is thought to give rise to grave—and in the view of some, insuperable—difficulties. Quine has two arguments against the intelligibility of de re modality: a “logical” and a “metaphysical” one. That the “logical” argument is central to Quine’s attack is surely indisputable. But my claim that it is his basic argument is, in effect, denied by Kit Fine. I can (and do) agree with Fine that there are some significant differences between the two arguments. The most important question, for my purposes, is whether he is right to claim that the two arguments have force independently of one another.

A Study of the Effect of Standard Laboratory Processing on Speed and Resolution of Three Black and White Aerial Films

1983 ◽  
Vol 37 (1) ◽  
pp. 3-10
Author(s):  
E. A. Fleming ◽  
M. Landreville ◽  
E. Nagy
Keyword(s):  
Type A ◽  
The Other ◽  
Small Scale ◽  
High Contrast ◽  
Aerial Photo ◽  
Standard Laboratory ◽  
Average Gradient ◽  
Black And White ◽  
Contrast Range ◽  
Film Speed

Three aerial films were tested using standard aerial photo laboratory processing procedures for three different chemistries. Relationships were established with respect to average gradient, speed, base plus fog, graininess and resolution for low, medium and high contrast targets. The films compared were Kodak Double-X type 2405, Kodak Plus-X type 2402 and Kodak Panatomic-X 2412. The processing was done in a Kodak Versamat processor using Type A, 885 and Versaflo chemistry. The results indicated that processing in 885 chemistry enhanced film speed. The versatility of Double-X in terms of speed and contrast range was demonstrated, however the resolution of Panatomic-X greatly exceeded that of either of the other two films and shows promise for small scale mapping photography.

Delayed Choice with Correlated Photons

1988 ◽  
Vol 43 (2) ◽  
pp. 110-114
Author(s):  
O. E. Rössler
Keyword(s):  
Quantum Mechanics ◽  
Choice Experiment ◽  
Foundations Of Quantum Mechanics ◽  
Type A ◽  
The Other ◽  
Delayed Choice ◽  
Epr Experiment ◽  
The One

Abstract A new experiment in the foundations of quantum mechanics is proposed. The existence of correlated photons -first seen by Wheeler -can be taken as a hint to devise a ‘‘double-wing’’ delayed choice experiment in Wheeler’s sense. A path choice (polarization choice) measurement made on the one side should then block an interference type measurement made on the other side (‘‘distant choice’’). A precondition for the combined measurement to work in theory is that the correlated photons used are of the ‘‘prepolarized’’ (Selleri) rather than the ‘‘unpolarized’’ (Böhm) type. A first EPR experiment involving prepolarized photons was recently performed by Alley and Shih. It may be used as a partial experiment within the proposed experiment.

scholarly journals Deontic Logics as Axiomatic Extensions of First-Order Predicate Logic: An Approach Inspired by Wolniewicz’s Formal Ontology of Situations

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 109 ◽  
Author(s):  
Malec
Keyword(s):  
Deontic Logic ◽  
Predicate Logic ◽  
The Other ◽  
Choice Situation ◽  
Formal Ontology ◽  
Legal Rules ◽  
First Order ◽  
The Third ◽  
Other Hand ◽  
First Order Predicate Logic

The aim of this article is to present a method of creating deontic logics as axiomatic theories built on first-order predicate logic with identity. In the article, these theories are constructed as theories of legal events or as theories of acts. Legal events are understood as sequences (strings) of elementary situations in Wolniewicz′s sense. On the other hand, acts are understood as two-element legal events: the first element of a sequence is a choice situation (a situation that will be changed by an act), and the second element of this sequence is a chosen situation (a situation that arises as a result of that act). In this approach, legal rules (i.e., orders, bans, permits) are treated as sets of legal events. The article presents four deontic systems for legal events: AEP, AEPF, AEPOF, AEPOFI. In the first system, all legal events are permitted; in the second, they are permitted or forbidden; in the third, they are permitted, ordered or forbidden; and in the fourth, they are permitted, ordered, forbidden or irrelevant. Then, we present a deontic logic for acts (AAPOF), in which every act is permitted, ordered or forbidden. The theorems of this logic reflect deontic relations between acts as well as between acts and their parts. The direct inspiration to develop the approach presented in the article was the book Ontology of Situations by Boguslaw Wolniewicz, and indirectly, Wittgenstein’s Tractatus Logico-Philosophicus.

scholarly journals Pyranoanthocyanin Derived Pigments in Wine: Structure and Formation during Winemaking

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Ana Marquez ◽  
María P. Serratosa ◽  
Julieta Merida
Keyword(s):  
Pyruvic Acid ◽  
Formation Process ◽  
Second Generation ◽  
Type A ◽  
Enol Form ◽  
Hydroxycinnamic Acids ◽  
The Other ◽  
Yeast Fermentation ◽  
Type B ◽  
Initial Compound

In recent years many studies have been carried out on new pigments derived from anthocyanins that appear in wine during processing and aging. This paper aims to summarize the latest research on these compounds, focusing on the structure and the formation process. The main pyranoanthocyanins are formed from the reaction between the anthocyanins and some metabolites released during the yeast fermentation: carboxypyranoanthocyanins or type A vitisins, formed upon the reaction between the enol form of the pyruvic acid and the anthocyanins; type B vitisins, formed by the cycloaddition of an acetaldehyde molecule on an anthocyanin; methylpyranoanthocyanins, resulted from the reaction between acetone and anthocyanins; pinotins resulted from the covalent reaction between the hydroxycinnamic acids and anthocyanins; and finally flavanyl-pyranoanthocyanins. On the other hand, the second generation of compounds has also been reviewed, where the initial compound is a pyranoanthocyanin. This family includes oxovitisins, vinylpyranoanthocyanins, pyranoanthocyanins linked through a butadienylidene bridge, and pyranoanthocyanin dimers.

Intermediate predicate logics determined by ordinals

1990 ◽  
Vol 55 (3) ◽  
pp. 1099-1124 ◽  
Author(s):  
Pierluigi Minari ◽  
Mitio Takano ◽  
Hiroakira Ono
Keyword(s):  
Predicate Logic ◽  
The Other ◽  
Constant Domain ◽  
Kripke Frames ◽  
Other Hand ◽  
Countable Ordinal ◽  
Intermediate Predicate Logics ◽  
Regular Ordinal

AbstractFor each ordinal α > 0, L(α) is the intermediate predicate logic characterized by the class of all Kripke frames with the poset α and with constant domain. This paper will be devoted to a study of logics of the form L(α). It will be shown that for each uncountable ordinal of the form α + η with a finite or a countable η(> 0), there exists a countable ordinal of the form β + η such that L(α + η) = L(β + η). On the other hand, such a reduction of ordinals to countable ones is impossible for a logic L(α) if α is an uncountable regular ordinal. Moreover, it will be proved that the mapping L is injective if it is restricted to ordinals less than ωω, i.e. α ≠ β implies L(α) ≠ L(β) for each ordinal α, β ≤ ωω.

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