Analytic cut

1969 ◽  
Vol 33 (4) ◽  
pp. 560-564 ◽  
Author(s):  
Raymond M. Smullyan
Keyword(s):  
Propositional Logic ◽  
Inference Rule ◽  
The Other ◽  
Inference Rules ◽  
Quantification Theory ◽  
The Real ◽  
Gentzen Systems ◽  
Real Importance ◽  
Per Se ◽  
Axiom Systems

The real importance of cut-free proofs is not the elimination of cuts per se, but rather that such proofs obey the subformula principle. In this paper we accomplish this latter objective in a different manner.In the usual formulations of Gentzen systems, there is only one axiom scheme; all the other postulates are inference rules. By contrast, we consider here some Gentzen type axiom systems for propositional logic and Quantification Theory in which there is only one inference rule; all the other postulates are axiom schemes. This admits of an unusually elegant axiomatization of logic.

Correspondences between gentzen and hilbert systems

2006 ◽  
Vol 71 (3) ◽  
pp. 903-957 ◽  
Author(s):  
J.G. Raftery
Keyword(s):  
The Other ◽  
Inference Rules ◽  
Consequence Relation ◽  
Formal Systems ◽  
Gentzen Systems ◽  
Other Hand

Most Gentzen systems arising in logic contain few axiom schemata and many rule schemata. Hilbert systems, on the other hand, usually contain few proper inference rules and possibly many axioms. Because of this, the two notions tend to serve different purposes. It is common for a logic to be specified in the first instance by means of a Gentzen calculus, whereupon a Hilbert-style presentation ‘for’ the logic may be sought—or vice versa. Where this has occurred, the word ‘for’ has taken on several different meanings, partly because the Gentzen separator ⇒ can be interpreted intuitively in a number of ways. Here ⇒ will be denoted less evocatively by ⊲.In this paper we aim to discuss some of the useful ways in which Gentzen and Hilbert systems may correspond to each other. Actually, we shall be concerned with the deducibility relations of the formal systems, as it is these that are susceptible to transformation in useful ways. To avoid potential confusion, we shall speak of Hilbert and Gentzen relations. By a Hilbert relation we mean any substitution-invariant consequence relation on formulas—this comes to the same thing as the deducibility relation of a set of Hilbert-style axioms and rules. By a Gentzen relation we mean the fully fledged generalization of this notion in which sequents take the place of single formulas. In the literature, Hilbert relations are often referred to as sentential logics. Gentzen relations as defined here are their exact sequential counterparts.

Logical consecutions in discrete linear temporal logic

2005 ◽  
Vol 70 (4) ◽  
pp. 1137-1149 ◽  
Author(s):  
V. V. Rybakov
Keyword(s):  
Temporal Logic ◽  
Propositional Logic ◽  
Inference Rule ◽  
Logical Consequence ◽  
Linear Temporal Logic ◽  
Inference Rules ◽  
Temporal Logics ◽  
Temporal Inference ◽  
Semantic Techniques ◽  
The Given

AbstractWe investigate logical consequence in temporal logics in terms of logical consecutions, i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be ‘correct’ in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L ≤, ≥〉 of all integer numbers, is the prime object of our investigation. We describe consecutions admissible in LDTL in a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible in LDTL. Also, we note that using the same technique it follows that the linear temporal logic L(N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logics LDTL and L(N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (known fact), and the given deciding algorithms are explicit.

Hidden “holes” in the capital of banks and the supply of credit to the real sector of economy

2018 ◽  
pp. 49-68 ◽  
Author(s):  
M. E. Mamonov
Keyword(s):  
Credit Risk ◽  
The Other ◽  
Real Sector ◽  
Capital Management ◽  
Loan Loss ◽  
Short Term ◽  
The Real ◽  
Ex Post ◽  
The One

Our analysis documents that the existence of hidden “holes” in the capital of not yet failed banks - while creating intertemporal pressure on the actual level of capital - leads to changing of maturity of loans supplied rather than to contracting of their volume. Long-term loans decrease, whereas short-term loans rise - and, what is most remarkably, by approximately the same amounts. Standardly, the higher the maturity of loans the higher the credit risk and, thus, the more loan loss reserves (LLP) banks are forced to create, increasing the pressure on capital. Banks that already hide “holes” in the capital, but have not yet faced with license withdrawal, must possess strong incentives to shorten the maturity of supplied loans. On the one hand, it raises the turnovers of LLP and facilitates the flexibility of capital management; on the other hand, it allows increasing the speed of shifting of attracted deposits to loans to related parties in domestic or foreign jurisdictions. This enlarges the potential size of ex post revealed “hole” in the capital and, therefore, allows us to assume that not every loan might be viewed as a good for the economy: excessive short-term and insufficient long-term loans can produce the source for future losses.

The Problem of the Typology of Rationality in Muslim Culture

2019 ◽  
Vol 62 (6) ◽  
pp. 88-99
Author(s):  
Andrey A. Lukashev
Keyword(s):  
Modern Philosophy ◽  
Theoretical Basis ◽  
Theoretical Models ◽  
The Other ◽  
Common Denominator ◽  
Islamic Culture ◽  
The Common ◽  
Per Se ◽  
The One ◽  
Muslim Culture

The typology of rationality is one of major issues of modern philosophy. In an attempt to provide a typology to Oriental materials, a researcher faces additional problems. The diversity of the Orient as such poses a major challenge. When we say “Oriental,” we mean several cultures for which we cannot find a common denominator. The concept of “Orient” involves Arabic, Indian, Chinese, Turkish and other cultures, and the only thing they share is that they are “non-Western.” Moreover, even if we focus just on Islamic culture and look into rationality in this context, we have to deal with a conglomerate of various trends, which does not let us define, with full confidence, a common theoretical basis and treat them as a unity. Nevertheless, we have to go on trying to find common directions in thought development, so as to draw conclusions about types of rationality possible in Islamic culture. A basis for such a typology of rationality in the context of the Islamic world was recently suggested in A.V. Smirnov’s logic of sense theory. However, actual empiric material cannot always fit theoretical models, and the cases that do not fit the common scheme are interesting per se. On the one hand, examination of such cases gives an opportunity to specify certain provisions of the theory and, on the other hand, to define the limits of its applicability.

Hilbert-style proof Calculus for Propositional Logic in ABC notation

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Propositional Logic ◽  
Inference Rule ◽  
Modus Ponens ◽  
Axiomatic System ◽  
First Contact

All nine axioms and a single inference rule of logic (Modus Ponens) within the Hilbert axiomatic system are presented using capital letters (ABC) in order to familiarize the beginner student in hers/his first contact with the topic.

scholarly journals Stochastic Processes with a Particular Type of Variograms

2007 ◽  
Vol 2007 ◽  
pp. 1-5 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Stochastic Processes ◽  
Series Expansion ◽  
Real Line ◽  
Random Fields ◽  
The Other ◽  
Simple Construction ◽  
The Real ◽  
Line Form

This paper is concerned with a class of stochastic processes or random fields with second-order increments, whose variograms have a particular form, among which stochastic processes having orthogonal increments on the real line form an important subclass. A natural issue, how big this subclass is, has not been explicitly addressed in the literature. As a solution, this paper characterizes a stochastic process having orthogonal increments on the real line in terms of its variogram or its construction. Our findings are a little bit surprising: this subclass is big in terms of the variogram, and on the other hand, it is relatively “small” according to a simple construction. In particular, every such process with Gaussian increments can be simply constructed from Brownian motion. Using the characterizations we obtain a series expansion of the stochastic process with orthogonal increments.

scholarly journals GazeEMD: Detecting Visual Intention in Gaze-Based Human-Robot Interaction

Robotics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 68
Author(s):  
Lei Shi ◽  
Cosmin Copot ◽  
Steve Vanlanduit
Keyword(s):  
Cognitive Load ◽  
Real World ◽  
Robotic Manipulator ◽  
Similarity Score ◽  
Human Robot Interaction ◽  
Experimental Results ◽  
The Other ◽  
Robot Interaction ◽  
Run Length ◽  
The Real

In gaze-based Human-Robot Interaction (HRI), it is important to determine human visual intention for interacting with robots. One typical HRI interaction scenario is that a human selects an object by gaze and a robotic manipulator will pick up the object. In this work, we propose an approach, GazeEMD, that can be used to detect whether a human is looking at an object for HRI application. We use Earth Mover’s Distance (EMD) to measure the similarity between the hypothetical gazes at objects and the actual gazes. Then, the similarity score is used to determine if the human visual intention is on the object. We compare our approach with a fixation-based method and HitScan with a run length in the scenario of selecting daily objects by gaze. Our experimental results indicate that the GazeEMD approach has higher accuracy and is more robust to noises than the other approaches. Hence, the users can lessen cognitive load by using our approach in the real-world HRI scenario.

scholarly journals Distribution of rational points on the real line

1973 ◽  
Vol 15 (2) ◽  
pp. 243-256 ◽  
Author(s):  
T. K. Sheng
Keyword(s):  
Algebraic Number ◽  
Rational Number ◽  
Real Line ◽  
Rational Points ◽  
The Other ◽  
Liouville Numbers ◽  
The Real ◽  
Other Hand ◽  
Image Position

It is well known that no rational number is approximable to order higher than 1. Roth [3] showed that an algebraic number is not approximable to order greater than 2. On the other hand it is easy to construct numbers, the Liouville numbers, which are approximable to any order (see [2], p. 162). We are led to the question, “Let Nn(α, β) denote the number of distinct rational points with denominators ≦ n contained in an interval (α, β). What is the behaviour of Nn(α, + 1/n) as α varies on the real line?” We shall prove that and that there are “compressions” and “rarefactions” of rational points on the real line.

HALF-WAY TECHNOLOGIES ARE PROFITABLE

PEDIATRICS ◽  
1995 ◽  
Vol 95 (5) ◽  
pp. 681-681
Keyword(s):  
The Other ◽  
Other Hand ◽  
Per Se ◽  
Commercial Organizations

Decisive interventions, like vaccines, can be quite inexpensive. But commercial organizations make money by selling commodities; they cannot produce and sell "health" per se. The most profitable commodities are those embodying the "half-way" technologies, for those with the means to pay for them-again and again and again. Vaccines, on the other hand, "may never prove as enticing as drugs for pharmaceutical makers. They can be quite expensive to develop, and they produce less income-repeated refills not required ... "

II. Causa und titulus

2021 ◽  
Vol 138 (1) ◽  
pp. 83-179
Author(s):  
Eric H. Pool
Keyword(s):  
The Other ◽  
The Real

Abstract Causa and titulus. Qualifications of possession and a change of terminology in Ulp. D. 5,3,13,1. – In D. 5,3,13,1, Ulpian states that every title to possession (like pro emptore, pro donato etc.) could be accompanied by a general title pro possessore, which becomes decisive if the other title failed. The text is interesting in two aspects: First, it is one of only a handful of classical texts which speak of titulus instead of causa possessionis. Therefore, the text is still today suspected of interpolation. Second, it is heavily disputed which circumstances lead to a possession pro possessore and why this typolology is used at all. This article proposes a solution to both problems. The pro possessore terminology can only be assessed correctly if we focus the procedural position of the possessor, especially in the realm of the hereditatis petitio. The new terminology (titulus) is a mere consequence of the fact, that the burden of prove is assigned according to the ,title‘ of possession indicated by the possessor, not by the real (and possibly unprovable) cause.

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