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.

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.

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.

scholarly journals 4. Reasoning with Partial Knowledge

2002 ◽  
Vol 32 (1) ◽  
pp. 133-181 ◽  
Author(s):  
László Pólos ◽  
Michael T. Hannan
Keyword(s):  
Logical Consequence ◽  
Order Logic ◽  
First Order Logic ◽  
Partial Knowledge ◽  
Age Dependence ◽  
Consequence Relation ◽  
First Order ◽  
Correct Execution ◽  
Organizational Mortality ◽  
Monotonicity Principle

We investigate how sociological argumentation differs from classical first-order logic. We focus on theories about age dependence of organizational mortality. The overall pattern of argument does not comply with the classical monotonicity principle: Adding premises overturns conclusions in an argument. The cause of nonmonotonicity is the need to derive conclusions from partial knowledge. We identify metaprinciples that appear to guide the observed sociological argumentation patterns, and we formalize a semantics to represent them. This semantics yields a new kind of logical consequence relation. We demonstrate that this new logic can reproduce the results of informal sociological theorizing and lead to new insights. It allows us to unify existing theory fragments, and it paves the way toward a complete classical theory. Observed inferential patterns which seem “wrong” according to one notion of inference might just as well signal that the speaker is engaged in correct execution of another style of reasoning. —Johan van Benthem (1996)

Post-Non-Classical World View in the On-Screen Reality of the Digital Epoch

2015 ◽  
pp. 4-12
Author(s):  
Elena V. Nikolaeva
Keyword(s):  
World View ◽  
Dynamic Chaos ◽  
Digital Culture ◽  
Fractal Nature ◽  
Late 20Th Century ◽  
First Order ◽  
Classical World ◽  
Different Types ◽  
Strange Loops ◽  
Cultural World

The article analyzes the correlation between the screen reality and the first-order reality in the digital culture. Specific concepts of the scientific paradigm of the late 20th century are considered as constituent principles of the on-screen reality of the digital epoch. The study proves that the post-non-classical cultural world view, emerging from the dynamic “chaos” of informational and semantic rows of TV programs and cinematographic narrations, is of a fractal nature. The article investigates different types of fractality of the TV content and film plots, their inner and outer “strange loops” and artistic interpretations of the “butterfly effect”.

Quantitative Models of Motor Responses Subject to Longitudinal, Lateral, and Preview Constraints

1978 ◽  
Vol 20 (1) ◽  
pp. 35-39 ◽  
Author(s):  
Tarald O. Kvålseth
Keyword(s):  
Experimental Data ◽  
Motor Control ◽  
Linear Models ◽  
Movement Time ◽  
Arm Movements ◽  
Second Order ◽  
Motor Responses ◽  
First Order ◽  
Different Types ◽  
Index Of Difficulty

First- and second-order linear models of mean movement time for serial arm movements aimed at a target and subject to preview constraints and lateral constraints were formulated as extensions of the so-called Fitts's law of motor control. These models were validated on the basis of experimental data from five subjects and found to explain from 80% to 85% of the variation in movement time in the case of the first-order models and from 93% to 95% of such variation for the second-order models. Fitts's index of difficulty (ID) was generally found to contribute more to the movement time than did either the preview ID or the lateral ID defined. Of the different types of errors, target overshoots occurred far more frequently than undershoots.

scholarly journals Analysis of rail yard and terminal performances

2014 ◽  
Vol 8 (2) ◽  
pp. 178-200 ◽  
Author(s):  
Marin Marinov ◽  
Leonardo Di Giovanni ◽  
Giulia Bellisai ◽  
Julian Clevermann ◽  
Anastasia Mastellou ◽  
...  
Keyword(s):  
Comparative Analysis ◽  
Critical Points ◽  
Network Performance ◽  
Logical Consequence ◽  
Time Frame ◽  
Key Factors ◽  
Railway Network ◽  
Rail Infrastructure ◽  
Different Types ◽  
Junction Points

One of the latest trends in the transport field is the increasing interest for the rejuvenation of the railway. It is considered to be a logical consequence of the gradual switch towards a more sustainable future in transports. Terminals and stations are considered to be the junction points between the various lines that constitute the railway network and can simply be described as points of arrival, departure and interchange of passengers or commodities. The most commonly used indicators that measure the level of their performance are time and cost. This study aims at exploring possible improvements that could be implemented to the infrastructure and the operation of terminals and stations in order to increase the efficiency level. Firstly, drawing upon grounded theory about rail infrastructure and terminals, a description is conducted, followed by a comparative analysis of the different types of existing terminals and stations. Secondly, the suggested improvements are presented in accordance with their time frame completion. The main contribution of this study is to illustrate the high significance of terminals, stations and yards, acknowledging them as crucial parts of the railway network, because as characterized and demonstrated in this study, their performance are key factors to the whole network performance, making the identification of their critical points and respective possible solutions, the final objective of this paper. In addition to this, emphasis is given to the need of improving and developing the existing terminal infrastructure and operations.

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.

Resolution in type theory

1971 ◽  
Vol 36 (3) ◽  
pp. 414-432 ◽  
Author(s):  
Peter B. Andrews
Keyword(s):  
Set Theory ◽  
Type Theory ◽  
Higher Order ◽  
Order Logic ◽  
First Order Logic ◽  
Higher Order Logic ◽  
First Order ◽  
Different Types ◽  
Axiomatic Set Theory ◽  
Order Predicate Calculus

In [8] J. A. Robinson introduced a complete refutation procedure called resolution for first order predicate calculus. Resolution is based on ideas in Herbrand's Theorem, and provides a very convenient framework in which to search for a proof of a wff believed to be a theorem. Moreover, it has proved possible to formulate many refinements of resolution which are still complete but are more efficient, at least in many contexts. However, when efficiency is a prime consideration, the restriction to first order logic is unfortunate, since many statements of mathematics (and other disciplines) can be expressed more simply and naturally in higher order logic than in first order logic. Also, the fact that in higher order logic (as in many-sorted first order logic) there is an explicit syntactic distinction between expressions which denote different types of intuitive objects is of great value where matching is involved, since one is automatically prevented from trying to make certain inappropriate matches. (One may contrast this with the situation in which mathematical statements are expressed in the symbolism of axiomatic set theory.).

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