AGGREGATION AND IDEMPOTENCE

2013 ◽  
Vol 6 (4) ◽  
pp. 680-708 ◽  
Author(s):  
LLOYD HUMBERSTONE
Keyword(s):  
Propositional Logic ◽  
Consequence Relations ◽  
Classical Propositional Logic ◽  
Intuitionistic Propositional Logic ◽  
Sentential Context ◽  
Consequence Relation ◽  
Intermediate Logics ◽  
Conservative Operation ◽  
The One

AbstractA 1-ary sentential context is aggregative (according to a consequence relation) if the result of putting the conjunction of two formulas into the context is a consequence (by that relation) of the results of putting first the one formula and then the other into that context. All 1-ary contexts are aggregative according to the consequence relation of classical propositional logic (though not, for example, according to the consequence relation of intuitionistic propositional logic), and here we explore the extent of this phenomenon, generalized to having arbitrary connectives playing the role of conjunction; among intermediate logics, LC, shows itself to occupy a crucial position in this regard, and to suggest a characterization, applicable to a broader range of consequence relations, in terms of a variant of the notion of idempotence we shall call componentiality. This is an analogue, for the consequence relations of propositional logic, of the notion of a conservative operation in universal algebra.

scholarly journals THE UBIQUITY OF CONSERVATIVE TRANSLATIONS

2012 ◽  
Vol 5 (4) ◽  
pp. 666-678 ◽  
Author(s):  
EMIL JEŘÁBEK
Keyword(s):  
Propositional Logic ◽  
Broad Class ◽  
Paraconsistent Logic ◽  
Lambek Calculus ◽  
Classical Propositional Logic ◽  
Consequence Relation ◽  
Deductive Systems ◽  
Nonclassical Logics ◽  
Conservative Translations

AbstractWe study the notion of conservative translation between logics introduced by (Feitosa & D’Ottaviano2001). We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas can be conservatively translated into CPC. The translation is computable if the consequence relation is decidable. More generally, we show that one can take instead of CPC a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including most nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other. We also provide some counterexamples, in particular the paraconsistent logic LP is not universal.

CLASSICALLY ARCHETYPAL RULES

2018 ◽  
Vol 11 (2) ◽  
pp. 279-294 ◽  
Author(s):  
TOMASZ POŁACIK ◽  
LLOYD HUMBERSTONE
Keyword(s):  
Propositional Logic ◽  
General Notion ◽  
Classical Propositional Logic ◽  
Consequence Relation

AbstractA one-premiss rule is said to be archetypal for a consequence relation when not only is the conclusion of any application of the rule a consequence (according to that relation) of the premiss, but whenever one formula has another as a consequence, these formulas are respectively equivalent to a premiss and a conclusion of some application of the rule. We are concerned here with the consequence relation of classical propositional logic and with the task of extending the above notion of archetypality to rules with more than one premiss, and providing an informative characterization of the set of rules falling under the more general notion.

Implication with possible exceptions

2001 ◽  
Vol 66 (2) ◽  
pp. 517-535
Author(s):  
Herman Jurjus ◽  
Harrie de Swart
Keyword(s):  
Propositional Logic ◽  
Modus Ponens ◽  
The Other ◽  
Classical Propositional Logic ◽  
Consequence Relation ◽  
Other Hand

AbstractWe introduce an implication-with-possible-exceptions and define validity of rules-with-possible-exceptions by means of the topological notion of a full subset. Our implication-with-possible-exceptions characterises the preferential consequence relation as axiomatized by Kraus, Lehmann and Magidor [Kraus, Lehmann, and Magidor, 1990]. The resulting inference relation is non-monotonic. On the other hand, modus ponens and the rule of monotony, as well as all other laws of classical propositional logic, are valid-up-to-possible exceptions. As a consequence, the rules of classical propositional logic do not determine the meaning of deducibility and inference as implication-without-exceptions.

Logical connectives for intuitionistic propositional logic

1971 ◽  
Vol 36 (1) ◽  
pp. 15-20 ◽  
Author(s):  
Dean P. McCullough
Keyword(s):  
Intuitionistic Logic ◽  
Propositional Logic ◽  
Classical Type ◽  
Classical Propositional Logic ◽  
Intuitionistic Propositional Logic ◽  
Truth Function ◽  
Logical Connectives ◽  
Complete Set ◽  
Complete Sets

In classical propositional logic it is well known that {7, ⊃ } is a functionally complete set with respect to a two-valued truth function modeling. I.e. all definable logical connectives are definable from 7 and ⊃. Other modelings of classical type propositional logics may have different functionally complete sets; for example, multivalued truth function modelings.This paper examines the question of a functionally complete set of logical connectives for intuitionistic propositional logic with respect to S. Kripke's modeling for intuitionistic logic.

scholarly journals A Syntactic Characterization of the Gabbay-de Jongh Logics

10.29007/1mcd ◽  
2018 ◽  
Author(s):  
Jeroen Goudsmit
Keyword(s):  
Propositional Logic ◽  
Sufficient Conditions ◽  
Intuitionistic Propositional Logic ◽  
Admissible Rules ◽  
Intermediate Logics ◽  
Refutation Systems ◽  
Refutation System

Skura syntactically characterised intuitionistic propositional logic among all intermediate logics by means of a Łukasiewicz-style refutation system. Another such syntactic characterisation is given by Iemhoff in terms of admissible rules. Here we offer a bridge between these results. That is to say, we provide sufficient conditions under which admissible rules yield a refutation system fully characterising the logic. In particular, we give a characterisation of the Gabbay–de Jongh logics by means of refutation systems employing ideas from admissibility.

You Are the One I Want to Communicate With!

2013 ◽  
Vol 44 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Sabrina Pierucci ◽  
Olivier Klein ◽  
Andrea Carnaghi
Keyword(s):  
Memory Bias ◽  
Shared Reality ◽  
Communication Partner ◽  
Shared Reality Theory ◽  
The One ◽  
Study Participants

This article investigates the role of relational motives in the saying-is-believing effect ( Higgins & Rholes, 1978 ). Building on shared reality theory, we expected this effect to be most likely when communicators were motivated to “get along” with the audience. In the current study, participants were asked to describe an ambiguous target to an audience who either liked or disliked the target. The audience had been previously evaluated as a desirable vs. undesirable communication partner. Only participants who communicated with a desirable audience tuned their messages to suit their audience’s attitude toward the target. In line with predictions, they also displayed an audience-congruent memory bias in later recall.

The Formation of Intermediate Product I in a Purified System The Role of Factor IX or of its Precursor and of a Hageman Factor-PTA Fraction

1961 ◽  
Vol 6 (02) ◽  
pp. 224-234 ◽  
Author(s):  
E. T Yin ◽  
F Duckert
Keyword(s):  
Intermediate Product ◽  
Factor Ix ◽  
Assay Method ◽  
Lag Phase ◽  
Factor X ◽  
Haemophilia B ◽  
Hageman Factor ◽  
One Stage ◽  
The One

Summary1. The role of two clot promoting fractions isolated from either plasma or serum is studied in a purified system for the generation of intermediate product I in which the serum is replaced by factor X and the investigated fractions.2. Optimal generation of intermediate product I is possible in the purified system utilizing fractions devoid of factor IX one-stage activity. Prothrombin and thrombin are not necessary in this system.3. The fraction containing factor IX or its precursor, no measurable activity by the one-stage assay method, controls the yield of intermediate product I. No similar fraction can be isolated from haemophilia B plasma or serum.4. The Hageman factor — PTA fraction shortens the lag phase of intermediate product I formation and has no influence on the yield. This fraction can also be prepared from haemophilia B plasma or serum.

THE ROLE OF ANTHROPONYMS IN THE SEMANTIC FIELD OF ARTISTIC WORKS

2019 ◽  
Vol 2019 (29) ◽  
pp. 66-77
Author(s):  
Lidiya Derbenyova
Keyword(s):  
Literary Work ◽  
Main Theme ◽  
Semantic Field ◽  
New Meanings ◽  
Minor Part ◽  
The One ◽  
A Minor ◽  
And Storage ◽  
Horizon Of Expectations

The article explores the role of antropoetonyms in the reader’s “horizon of expectation” formation. As a kind of “text in the text”, antropoetonyms are concentrating a large amount of information on a minor part of the text, reflecting the main theme of the work. As a “text” this class of poetonyms performs a number of functions: transmission and storage of information, generation of new meanings, the function of “cultural memory”, which explains the readers’ “horizon of expectations”. In analyzing the context of the literary work we should consider the function of antropoetonyms in vertical context (the link between artistic and other texts, and the groundwork system of culture), as well as in the context of the horizontal one (times’ connection realized in the communication chain from the word to the text; the author’s intention). In this aspect, the role of antropoetonyms in the structure of the literary text is extremely significant because antropoetonyms convey an associative nature, generating a complex mechanism of allusions. It’s an open fact that they always transmit information about the preceding text and suggest a double decoding. On the one hand, the recipient decodes this information, on the other – accepts this as a sort of hidden, “secret” sense.

Public Procurement Principles Generated by the Treaty of Rome

2020 ◽  
Vol 26 (2) ◽  
pp. 217-223
Author(s):  
Ioan-Gabriel Popa
Keyword(s):  
European Economic Community ◽  
Public Procurement ◽  
Free Movement ◽  
European Directives ◽  
Community Institutions ◽  
Treaty Of Rome ◽  
General Principles Of Law ◽  
Free Movement Of Goods ◽  
The One

AbstractIn order to understand the principles of public procurement in Romania, it is necessary to analyze, on the one hand, the European directives that regulate the actual public procurement and, on the other hand, the context in which the European directives were adopted. Even with the directives in force, the more general provisions contained in the Treaty of the European Economic Community (EEC) in Rome, hereinafter referred to as the Treaty, are applied, as well as many more general principles of law that will guide the interpretation of these directives. The Treaty was adopted in Rome, in 1957 and became applicable from January 1, 1958. It is considered that the source of the principles of public procurement is the Treaty. Even if in Treaty contained no specific provisions regarding the field of public procurement, it reflects the principles and the general framework for the functioning of the single market, a market characterized through the prism of the fundamental freedoms established by the Treaty: the free movement of goods, services, capital and persons. As the field of public procurement is closely linked to the free movement of goods, this principle is promoted and implemented in the practice of this field based on the regulations, directives and decisions of the Community institutions. The role of the free movement of goods is to harmonize the relationships involved in the process of purchasing goods, but also to ensure the homogeneity, coherence and balance of this process.

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