New foundation of formal metamathematics

1938 ◽  
Vol 3 (1) ◽  
pp. 1-36 ◽  
Author(s):  
L. Chwistek ◽  
W. Hetper
Keyword(s):  
Ordinary Language ◽  
Modus Ponens ◽  
The Other ◽  
Other Hand

Our method is based on the same principles which we have assumed in a paper about the foundations of metamathematics which we published in collaboration with J. Herzberg some years ago. Nevertheless we have introduced some important modifications which enable us to use a very restricted preliminary language and to avoid any artificial construction.The problem of a restricted language in mathematics appears to be a very important one, as our ordinary language is really ambiguous and obscure. On the other hand there is the problem of restricting the intuitive logic to be used in our construction. We shall see that for this purpose we need only substitutions and modus ponens.If we avoided any abbreviation, we could reduce our preliminary language to propositions of the following forms:X is a theorem.If P, then Q.But we have to do with very long symbolic expressions and as there is not yet any machine to build up such expressions we must use abbreviations. For this purpose we shall use propositions of the following forms in the preliminary language:X is an expression.X is an abbreviation of Y.Any proposition which does not belong to one of our four forms will be excluded from our construction.

scholarly journals Forward and Backward Chaining with P Systems

2014 ◽  
pp. 149-158
Author(s):  
Sergiu Ivanov ◽  
Artiom Alhazov ◽  
Vladimir Rogojin ◽  
Miguel A. Gutiérrez-Naranjo
Keyword(s):  
Computer Science ◽  
Propositional Logic ◽  
Membrane Computing ◽  
Modus Ponens ◽  
The Other ◽  
P Systems ◽  
Backward Chaining ◽  
Other Hand

One of the concepts that lie at the basis of membrane computing is the multiset rewriting rule. On the other hand, the paradigm of rules is profusely used in computer science for representing and dealing with knowledge. Therefore, establishing a “bridge” between these domains is important, for instance, by designing P systems reproducing the modus ponens-based forward and backward chaining that can be used as tools for reasoning in propositional logic. In this paper, the authors show how powerful and intuitive the formalism of membrane computing is and how it can be used to represent concepts and notions from unrelated areas.

Frege and Natural Language

Philosophy ◽  
1985 ◽  
Vol 60 (234) ◽  
pp. 513-524 ◽  
Author(s):  
Andrew Rein
Keyword(s):  
Natural Language ◽  
Formal Language ◽  
Ordinary Language ◽  
The Other ◽  
Optical Instrument ◽  
Other Hand ◽  
Scientific Endeavour

It is a commonplace that Frege thought ordinary language to be seriously defective. Yet his remarks about ordinary language are not always unflattering. Comparing the relation between his formal language and ordinary language to the relation between the microscope and the eye, Frege remarked: ‘[the eye], because of the range of its applicability and because of the ease with which it can adapt itself to the most varied circumstances, has a great superiority over the microscope’. The point, of course, is that, for Frege, the deficiencies of ordinary language arise in connection with the scientific endeavour: ordinary language is not an acceptable medium in which to pursue truth. As he goes on to observe: ‘… viewed as an optical instrument [the eye] reveals many imperfections … as soon as scientific purposes place strong requirements upon sharpness of resolution, the eye proves to be inadequate. On the other hand, the microscope is perfectly suited for just such purposes’.

Metaphor

2009 ◽  
Author(s):  
Ted Cohen
Keyword(s):  
Figurative Language ◽  
Ordinary Language ◽  
The Other ◽  
Other Hand ◽  
Unified Description

Metaphor is one of a variety of uses of language in which what is communicated is not what the words mean literally. It is, therefore, so to speak, a way of speaking of something by talking about something else. Thus, one has said (or written) X and thereby communicated Y. This characteristic of ‘indirectness’ is not alone sufficient to distinguish metaphors from other non-standard uses of language, but there is also a question as to whether metaphors in general are sufficiently similar to one another to permit a single, unified description of them. On one hand, metaphor has been a feature of poetry for centuries, conspicuous in the work of Homer and Shakespeare and countless other poets. But on the other hand, metaphor is pervasive in ordinary language, both in speech and in writing. It is not obvious that a single account of metaphor could be adequate to both poetic and more prosaic uses of figurative language.

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.

scholarly journals Forward and Backward Chaining with P Systems

2011 ◽  
Vol 2 (2) ◽  
pp. 56-66 ◽  
Author(s):  
Sergiu Ivanov ◽  
Artiom Alhazov ◽  
Vladimir Rogojin ◽  
Miguel A. Gutiérrez-Naranjo
Keyword(s):  
Computer Science ◽  
Propositional Logic ◽  
Membrane Computing ◽  
Modus Ponens ◽  
The Other ◽  
P Systems ◽  
Backward Chaining ◽  
Other Hand

One of the concepts that lie at the basis of membrane computing is the multiset rewriting rule. On the other hand, the paradigm of rules is profusely used in computer science for representing and dealing with knowledge. Therefore, establishing a “bridge” between these domains is important, for instance, by designing P systems reproducing the modus ponens-based forward and backward chaining that can be used as tools for reasoning in propositional logic. In this paper, the authors show how powerful and intuitive the formalism of membrane computing is and how it can be used to represent concepts and notions from unrelated areas.

scholarly journals Forward and Backward Chaining with P Systems

2012 ◽  
pp. 1522-1531
Author(s):  
Sergiu Ivanov ◽  
Artiom Alhazov ◽  
Vladimir Rogojin ◽  
Miguel A. Gutiérrez-Naranjo
Keyword(s):  
Computer Science ◽  
Propositional Logic ◽  
Membrane Computing ◽  
Modus Ponens ◽  
The Other ◽  
P Systems ◽  
Backward Chaining ◽  
Other Hand

One of the concepts that lie at the basis of membrane computing is the multiset rewriting rule. On the other hand, the paradigm of rules is profusely used in computer science for representing and dealing with knowledge. Therefore, establishing a “bridge” between these domains is important, for instance, by designing P systems reproducing the modus ponens-based forward and backward chaining that can be used as tools for reasoning in propositional logic. In this paper, the authors show how powerful and intuitive the formalism of membrane computing is and how it can be used to represent concepts and notions from unrelated areas.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

Life Beyond 1MeV

1980 ◽  
Vol 38 ◽  
pp. 30-33
Author(s):  
K.H. Westmacott
Keyword(s):  
Electron Microscopy ◽  
Past Experience ◽  
The Other ◽  
Good Case ◽  
Other Hand ◽  
The U.S

Life beyond 1MeV – like life after 40 – is not too different unless one takes advantage of past experience and is receptive to new opportunities. At first glance, the returns on performing electron microscopy at voltages greater than 1MeV diminish rather rapidly as the curves which describe the well-known advantages of HVEM often tend towards saturation. However, in a country with a significant HVEM capability, a good case can be made for investing in instruments with a range of maximum accelerating voltages. In this regard, the 1.5MeV KRATOS HVEM being installed in Berkeley will complement the other 650KeV, 1MeV, and 1.2MeV instruments currently operating in the U.S. One other consideration suggests that 1.5MeV is an optimum voltage machine – Its additional advantages may be purchased for not much more than a 1MeV instrument. On the other hand, the 3MeV HVEM's which seem to be operated at 2MeV maximum, are much more expensive.

Can the Academic Self-Concept be Positive and Realistic?

2005 ◽  
Vol 19 (3) ◽  
pp. 129-132 ◽  
Author(s):  
Reimer Kornmann
Keyword(s):  
Academic Performance ◽  
Opposite Effect ◽  
Self Esteem ◽  
Point Of View ◽  
The Other ◽  
Self Concept ◽  
High Ability ◽  
Self Image ◽  
Other Hand

Summary: My comment is basically restricted to the situation in which less-able students find themselves and refers only to literature in German. From this point of view I am basically able to confirm Marsh's results. It must, however, be said that with less-able pupils the opposite effect can be found: Levels of self-esteem in these pupils are raised, at least temporarily, by separate instruction, academic performance however drops; combined instruction, on the other hand, leads to improved academic performance, while levels of self-esteem drop. Apparently, the positive self-image of less-able pupils who receive separate instruction does not bring about the potential enhancement of academic performance one might expect from high-ability pupils receiving separate instruction. To resolve the dilemma, it is proposed that individual progress in learning be accentuated, and that comparisons with others be dispensed with. This fosters a self-image that can in equal measure be realistic and optimistic.

Sign in / Sign up

Export Citation Format

Share Document