Renominative logics with extended renomination, equality and predicate complement

2019 ◽  
Vol 24 (1-2) ◽  
pp. 34-48
Author(s):  
Nikitchenko M.S. ◽  
◽  
Shkilniak O.S. ◽  
Shkilniak S.S. ◽  
Mamedov T.A. ◽  
...  
Keyword(s):  
Logical Consequence ◽  
Consequence Relations ◽  
New Class ◽  
Composition Algebras ◽  
Semantic Properties

A new class of program-oriented logical formalisms is investigated – renominative logics with extended renominations, equality predicates, and predicate complement composition. Composition algebras and languages of such logics are described; their semantic properties are investigated. For these logics, a number of logical consequence relations are proposed and investigated, in particular, the logical consequence relations with undefinedness conditions. Properties of these relations form the semantic basis for further construction of sequent-type calculi for the proposed logics.

Logical consequence relations in logics of monotone predicates and logics of antitone predicates

2017 ◽  
pp. 021-029
Author(s):  
O.S. Shkilniak ◽  
Keyword(s):  
Logical Consequence ◽  
Consequence Relations ◽  
Consequence Relation ◽  
First Order ◽  
Different Types ◽  
Composition Algebras

Logical consequence is one of the fundamental concepts in logic. In this paper we study logical consequence relations for program-oriented logical formalisms: pure first-order composition nominative logics of quasiary predicates. In our research we are giving special attention to different types of logical consequence relations in various semantics of logics of monotone predicates and logics of antitone predicates. For pure first-order logics of quasiary predicates we specify composition algebras of predicates, languages, interpretation classes (sematics) and logical consequence relations. We obtain the pairwise distinct relations: irrefutability consequence P |= IR , consequence on truth P |= T , consequence on falsity P |= F, strong consequence P |= TF in P-sеmantics of partial singlevalued predicates and strong consequence R |= TF in R-sеmantics of partial multi-valued predicates. Of the total of 20 of defined logical consequence relations in logics of monotone predicates and of antitone predicates, the following ones are pairwise distinct: PE |= IR, PE |= T, PE |= F, PE |= TF, RM |= T, RM |= F, RM |= TF. A number of examples showing the differences between various types of logical consequence relations is given. We summarize the results concerning the existence of a particular logical consequence relation for certain sets of formulas in a table and determine interrelations between different types of logical consequence relations.

Pure first-order logics of quasiary predicates

2016 ◽  
pp. 073-086
Author(s):  
M.S. Nikitchenko ◽  
◽  
О.S. Shkilniak ◽  
S.S. Shkilniak ◽  
◽  
...  
Keyword(s):  
Logical Consequence ◽  
Quantifier Elimination ◽  
Consequence Relations ◽  
First Order ◽  
Semantic Models ◽  
Composition Algebras ◽  
Characteristic Features

Pure first-order logics of partial and total, single-valued and multi-valued quasiary predicates are investigated. For these logics we describe semantic models and languages, giving special attention in our research to composition algebras of predicates and interpretation classes (sematics), and logical consequence relations for sets of formulas. For the defined relations a number of sequent type calculi is constructed; their characteristic features are extended conditions for sequent closure and original forms for quantifier elimination.

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.

Composition-nominative logics of free-quantifier levels

2016 ◽  
pp. 038-047
Author(s):  
S.S. Shkilniak ◽  
◽  
D.B. Volkovytskyi ◽  
Keyword(s):  
Logical Consequence ◽  
Semantic Models ◽  
Semantic Properties

Free-quantifier composition nominative logics of partial quasiary predicates are considered. We specify the following levels of these logics: renominative, renominative with predicates of weak equality, renominative with predicates of strong equality, free-quantifier, free-quantifier with composition of weak equality, free-quantifier with composition of strong equality. The paper is mainly dedicated to investigation ofNlogics of free-quantifier levels with equality. Languages and semantic models of such logics are described, their semantic properties are studied, in particular the properties of relations of logical consequence.

scholarly journals Logical consequence relations in logics of quasiary predicates

2016 ◽  
pp. 029-043 ◽  
Author(s):  
O.S. Shkilniak ◽  
Keyword(s):  
Classical Logic ◽  
Logical Consequence ◽  
Consequence Relations ◽  
Sequent Calculi ◽  
The Difference

Logical consequence is one of the most fundamental concepts in logic. A wide use of partial (sometimes many-valued as well) mappings in programming makes important the investigation of logics of partial and many-valued predicates and logical consequence relations for them. Such relations are a semantic base for a corresponding sequent calculi construction. In this paper we consider logical consequence relations for composition nominative logics of total single-valued, partial single-valued, total many-valued and partial many-valued quasiary predicates. Properties of the relations can be different for different classes of predicates; they coincide in the case of classical logic. Relations of the types T, F, TF, IR and DI were in-vestigated in the earlier works. Here we propose relations of the types TvF and С for logics of quasiary predicates. The difference between these two relations manifests already on the propositional level. Properties of logical consequence relations are specified for formulas and sets of formulas. We consider partial cases when one of the sets of formulas is empty. It is shown that relations P|=TvF and R|=С are non-transitive, some properties of decomposition of formulas are not true for R|=С, but at the same time the latter can be modelled through R|=TF. A number of examples demonstrates particularities and distinctions of the defined relations. We also establish a relationship among various logical consequence relations.

Sequent calculi of first-order logics of partial predicates with extended renominations and composition of predicate complement

2020 ◽  
pp. 182-197
Author(s):  
M.S. Nikitchenko ◽  
◽  
О.S. Shkilniak ◽  
S.S. Shkilniak ◽  
◽  
...  
Keyword(s):  
Existence Theorems ◽  
Logical Consequence ◽  
Consequence Relations ◽  
Sequent Calculi ◽  
First Order ◽  
Counter Model ◽  
Partial Predicates ◽  
Model Existence

We study new classes of program-oriented logical formalisms – pure first-order logics of quasiary predicates with extended renominations and a composition of predicate complement. For these logics, various logical consequence relations are specified and corresponding calculi of sequent type are constructed. We define basic sequent forms for the specified calculi and closeness conditions. The soundness, completeness, and counter-model existence theorems are proved for the introduced calculi.

In Situ microscopy of the anodic etching of silicon

1995 ◽  
Vol 53 ◽  
pp. 232-233
Author(s):  
Frances M. Ross ◽  
Peter C. Searson
Keyword(s):  
Composite Structures ◽  
High Surface ◽  
High Surface Area ◽  
Chemical Properties ◽  
Selective Etching ◽  
Silicon On Insulator ◽  
Second Phase ◽  
Porous Layers ◽  
New Class ◽  
Porous Semiconductors

Porous semiconductors represent a relatively new class of materials formed by the selective etching of a single or polycrystalline substrate. Although porous silicon has received considerable attention due to its novel optical properties1, porous layers can be formed in other semiconductors such as GaAs and GaP. These materials are characterised by very high surface area and by electrical, optical and chemical properties that may differ considerably from bulk. The properties depend on the pore morphology, which can be controlled by adjusting the processing conditions and the dopant concentration. A number of novel structures can be fabricated using selective etching. For example, self-supporting membranes can be made by growing pores through a wafer, films with modulated pore structure can be fabricated by varying the applied potential during growth, composite structures can be prepared by depositing a second phase into the pores and silicon-on-insulator structures can be formed by oxidising a buried porous layer. In all these applications the ability to grow nanostructures controllably is critical.

The microtubule associated protein (MAP) tau forms a new class of triple-stranded left-hand helical fibrous protein polymer

1992 ◽  
Vol 50 (1) ◽  
pp. 540-541
Author(s):  
G. C. Ruben ◽  
K. Iqbal ◽  
I. Grundke-Iqbal ◽  
H. Wisniewski ◽  
T. L. Ciardelli ◽  
...  
Keyword(s):  
Axial Ratio ◽  
Normal Structure ◽  
Paired Helical Filaments ◽  
Left Hand ◽  
New Class ◽  
Protein Polymer ◽  
Fibrous Protein ◽  
Protein Map ◽  
Neurotransmitter Transport ◽  
Alzheimer Neurofibrillary Tangles

In neurons, the microtubule associated protein, tau, is found in the axons. Tau stabilizes the microtubules required for neurotransmitter transport to the axonal terminal. Since tau has been found in both Alzheimer neurofibrillary tangles (NFT) and in paired helical filaments (PHF), the study of tau's normal structure had to preceed TEM studies of NFT and PHF. The structure of tau was first studied by ultracentrifugation. This work suggested that it was a rod shaped molecule with an axial ratio of 20:1. More recently, paraciystals of phosphorylated and nonphosphoiylated tau have been reported. Phosphorylated tau was 90-95 nm in length and 3-6 nm in diameter where as nonphosphorylated tau was 69-75 nm in length. A shorter length of 30 nm was reported for undamaged tau indicating that it is an extremely flexible molecule. Tau was also studied in relation to microtubules, and its length was found to be 56.1±14.1 nm.

Study of segregation in La1.8Sr0.2CuO4 superconductor by STEM-EDS microanalysis

1987 ◽  
Vol 45 ◽  
pp. 54-55
Author(s):  
T. F. Kelly ◽  
P. J. Lee ◽  
E. E. Hellstrom ◽  
D. C. Larbalestier
Keyword(s):  
Rare Earth ◽  
High Field ◽  
Transport Current ◽  
Total Thickness ◽  
New Class ◽  
Ceramic Superconductors ◽  
Current Densities ◽  
Group Ii ◽  
Eds Microanalysis

Recently there has been much excitement over a new class of high Tc (>30 K) ceramic superconductors of the form A1-xBxCuO4-x, where A is a rare earth and B is from Group II. Unfortunately these materials have only been able to support small transport current densities 1-10 A/cm2. It is very desirable to increase these values by 2 to 3 orders of magnitude for useful high field applications. The reason for these small transport currents is as yet unknown. Evidence has, however, been presented for superconducting clusters on a 50-100 nm scale and on a 1-3 μm scale. We therefore planned a detailed TEM and STEM microanalysis study in order to see whether any evidence for the clusters could be seen.A La1.8Sr0.2Cu04 pellet was cut into 1 mm thick slices from which 3 mm discs were cut. The discs were subsequently mechanically ground to 100 μm total thickness and dimpled to 20 μm thickness at the center.

Electronic structure studies of conducting polymers by electron energy-loss spectroscopy

1996 ◽  
Vol 54 ◽  
pp. 160-161
Author(s):  
J. Fink
Keyword(s):  
Electronic Structure ◽  
Conducting Polymers ◽  
Conjugated Polymers ◽  
Electron Acceptors ◽  
Electron Donors ◽  
Light Emitting ◽  
One Dimensional ◽  
New Class ◽  
Electrical Conductivities ◽  
Electron Energy Loss

Conducting polymers comprises a new class of materials achieving electrical conductivities which rival those of the best metals. The parent compounds (conjugated polymers) are quasi-one-dimensional semiconductors. These polymers can be doped by electron acceptors or electron donors. The prototype of these materials is polyacetylene (PA). There are various other conjugated polymers such as polyparaphenylene, polyphenylenevinylene, polypoyrrole or polythiophene. The doped systems, i.e. the conducting polymers, have intersting potential technological applications such as replacement of conventional metals in electronic shielding and antistatic equipment, rechargable batteries, and flexible light emitting diodes.Although these systems have been investigated almost 20 years, the electronic structure of the doped metallic systems is not clear and even the reason for the gap in undoped semiconducting systems is under discussion.

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