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From Logic to Ontology: The limit of “The Semantic Web”

 

 

(Some post are written in English and Spanish language) 

http://www.linkedin.com/answers/technology/web-development/TCH_WDD/165684-18926951 

From Logic to Ontology: The limit of “The Semantic Web” 

 http://en.wikipedia.org/wiki/Undecidable_problem#Other_problems

If you read the next posts on this blog: 

Semantic Web

The Semantic Web

What is the Semantic Web, Actually?

The Metaweb: Beyond Weblogs. From the Metaweb to the Semantic Web: A Roadmap

Semantics to the people! ontoworld

What’s next for the Internet

Web 3.0: Update

How the Wikipedia 3.0: The End of Google? article reached 2 million people in 4 days!

Google vs Web 3.0

Google dont like Web 3.0 [sic] Why am I not surprised?

Designing a better Web 3.0 search engine

From semantic Web (3.0) to the WebOS (4.0)

Search By Meaning

A Web That Thinks Like You

MINDING THE PLANET: THE MEANING AND FUTURE OF THE SEMANTIC WEB

The long-promised “semantic” web is starting to take shape

Start-Up Aims for Database to Automate Web Searching

Metaweb: a semantic wiki startup

http://www.freebase.com/

The Semantic Web, Collective Intelligence and Hyperdata.

Informal logic 

Logical argument

Consistency proof 

Consistency proof and completeness: Gödel’s incompleteness theorems

Computability theory (computer science): The halting problem

Gödel’s incompleteness theorems: Relationship with computability

Non-formal or Inconsistency Logic: LACAN’s LOGIC. Gödel’s incompleteness theorems,

You will realize the internal relationship between them linked from Logic to Ontology.  

I am writing from now on an article about the existence of the semantic web.  

I will prove that it does not exist at all, and that it is impossible to build from machines like computers.  

It does not depend on the software and hardware you use to build it: You cannot do that at all! 

You will notice the internal relations among them, and the connecting thread is the title of this post: “Logic to ontology.”   

I will prove that there is no such construction, which can not be done from the machines, and that does not depend on the hardware or software used.  

More precisely, the limits of the semantic web are not set by the use of machines themselves and biological systems could be used to reach this goal, but as the logic that is being used to construct it does not contemplate the concept of time, since it is purely formal logic and metonymic lacks the metaphor, and that is what Gödel’s theorems remark, the final tautology of each construction or metonymic language (mathematical), which leads to inconsistencies. 

This consistent logic is completely opposite to the logic that makes inconsistent use of time, inherent of human unconscious, but the use of time is built on the lack, not on positive things, it is based on denials and absences, and that is impossible to reflect on a machine because of the perceived lack of the required self-awareness is acquired with the absence.  

The problem is we are trying to build an intelligent system to replace our way of thinking, at least in the information search, but the special nature of human mind is the use of time which lets human beings reach a conclusion, therefore does not exist in the human mind the halting problem or stop of calculation.  

So all efforts faced toward semantic web are doomed to failure a priori if the aim is to extend our human way of thinking into machines, they lack the metaphorical speech, because only a mathematical construction, which will always be tautological and metonymic, and lacks the use of the time that is what leads to the conclusion or “stop”.  

As a demonstration of that, if you suppose it is possible to construct the semantic web, as a language with capabilities similar to human language, which has the use of time, should we face it as a theorem, we can prove it to be false with a counter example, and it is given in the particular case of the Turing machine and “the halting problem”.  

Then as the necessary and sufficient condition for the theorem is not fulfilled, we still have the necessary condition that if a language uses time, it lacks formal logic, the logic used is inconsistent and therefore has no stop problem.

This is a necessary condition for the semantic web, but it is not enough and therefore no machine, whether it is a Turing Machine, a computer or a device as random as a black body related to physics field, can deal with any language other than mathematics language hence it is implied that this language is forced to meet the halting problem, a result of Gödel theorem.   

De la lógica a la ontología: El límite de la “web semántica”  

Si lee los siguientes artículos de este blog: 

http://es.wikipedia.org/wiki/Web_sem%C3%A1ntica  

Wikipedia 3.0: El fin de Google (traducción Spanish)

Lógica 

Lógica Consistente y completitud: Teoremas de la incompletitud de Gödel (Spanish)

Consistencia lógica (Spanish)

Teoría de la computabilidad. Ciencia de la computación.

Teoremas de la incompletitud de Gödel y teoría de la computación: Problema de la parada 

Lógica inconsistente e incompletitud: LOGICAS LACANIANAS y Teoremas de la incompletitud de Gödel (Spanish)  

Jacques Lacan (Encyclopædia Britannica Online)

Usted puede darse cuenta de las relaciones internas entre ellos, y el hilo conductor es el título de este mismo post: “de la lógica a la ontología”.  

Probaré que no existe en absoluto tal construcción, que no se puede hacer desde las máquinas, y que no depende ni del hardware ni del software utilizado.   

Matizando la cuestión, el límite de la web semántica está dado no por las máquinas y/o sistemas biológicos que se pudieran usar, sino porque la lógica con que se intenta construir carece del uso del tiempo, ya que la lógica formal es puramente metonímica y carece de la metáfora, y eso es lo que marcan los teoremas de Gödel, la tautología final de toda construcción y /o lenguaje metonímico (matemático), que lleva a contradicciones.  

Esta lógica consistente es opuesta a la lógica inconsistente que hace uso del tiempo, propia del insconciente humano, pero el uso del tiempo está construido en base a la falta, no en torno a lo positivo sino en base a negaciones y ausencias, y eso es imposible de reflejar en una máquina porque la percepción de la falta necesita de la conciencia de sí mismo que se adquiere con la ausencia.   

El problema está en que pretendemos construir un sistema inteligente que sustituya nuestro pensamiento, al menos en las búsquedas de información, pero la particularidad de nuestro pensamiento humano es el uso del tiempo el que permite concluir, por eso no existe en la mente humana el problema de la parada o detención del cálculo, o lo que es lo mismo ausencia del momento de concluir.  

Así que todos los esfuerzos encaminados a la web semántica están destinados al fracaso a priori si lo que se pretende es prolongar nuestro pensamiento humano en las máquinas, ellas carecen de discurso metafórico, pues sólo son una construcción matemática, que siempre será tautológica y metonímica, ya que además carece del uso del tiempo que es lo que lleva al corte, la conclusión o la “parada”.  

Como demostración vale la del contraejemplo, o sea que si suponemos que es posible construir la web semántica, como un lenguaje con capacidades similares al lenguaje humano, que tiene el uso del tiempo, entonces si ese es un teorema general, con un solo contraejemplo se viene abajo, y el contraejemplo está dado en el caso particular de la máquina de Turing y el “problema de la parada”.  

Luego no se cumple la condición necesaria y suficiente del teorema, nos queda la condición necesaria que es que si un lenguaje tiene el uso del tiempo, carece de lógica formal, usa la lógica inconsistente y por lo tanto no tiene el problema de la parada”, esa es condición necesaria para la web semántica, pero no suficiente y por ello ninguna máquina, sea de Turing, computador o dispositivo aleatorio como un cuerpo negro en física, puede alcanzar el uso de un lenguaje que no sea el matemático con la paradoja de la parada, consecuencia del teorema de Gödel.

Jacques Lacan (Encyclopædia Britannica Online)

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Logical argument

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This article is about arguments in logic. For other uses, see argument.

In logic, an argument is a set of declarative sentences (statements) known as the premises, and another declarative sentence (statement) known as the conclusion in which it is asserted that the truth of the conclusion follows from (is entailed by) the premisses. Such an argument may or may not be valid. Note: in logic declarative sentences (statements) are either true or false (not valid or invalid); arguments are valid or invalid (not true or false). Many authors in logic now use the term ‘sentence‘ to mean a declarative sentence rather than ‘statement‘ or ‘proposition‘ to avoid certain philosophical implications of these last two terms.

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[edit] Validity

A valid argument is one in which a specific structure is followed. An invalid argument is one in which a specfic structure is NOT followed.

The validity of an argument does not guarantee the truth of its conclusion, since a valid argument may have false premises. Only a valid argument with true premises must have a true conclusion.
The validity of an argument depends on its form, not on the truth or falsity of its premises and conclusions. Logic seeks to discover the forms of valid arguments. Since a valid argument is one such that if the premises are true then the conclusion must be true it follows that a valid argument cannot have true premises and a false conclusion. Since the validity of an argument depends on its form, an argument can be shown to be invalid by showing that its form is invalid because other arguments of the same form have true premises and false conclusions. In informal logic this is called a counter argument.

[edit] Proof

A proof is a demonstration that an argument is valid (see Proof procedure).

[edit] Validity, soundness and effectiveness

Some authors define a sound argument is a valid argument with true premises (see also Validity, Soundness, Truth.)

Arguments can be invalid for a variety of reasons. There are well-established patterns of reasoning that arguments may follow which render them invalid; these patterns are known as logical fallacies.

Even if an argument is sound (and hence also valid), an argument may still fail in its primary task of persuading us of the truth of its conclusion. Such an argument is then sound, but ineffective. An argument may fail to be effective because it is not scrutinizable, in the sense that it is not open to public examination. This may be because the argument is too long or too complex, because the terms occurring in it are obscure, or because the reasoning it employs is not well understood. The validity and soundness of an argument are logical properties of it, known as semantic properties. Effectiveness, on the other hand, is not a logical notion but a practical concern.

[edit] Formal arguments and mathematical arguments

In mathematics, an argument can often be formalized by writing each of its statements in a formal language such as first-order Peano Arithmetic. A formalized argument should have the following properties:

  • its premises are clearly identified as such
  • each of the inferences is justified by appeal to a specific rule of reasoning of the formal language in which the argument is written
  • the conclusion of the argument appears as the final inference

Checking the validity of a formal argument is thus a straightforward matter, since the presence of these three properties is easily verified.

Most arguments used in mathematics are not formal in quite so strict a sense. Strictly formal proofs of all but the most trivial assertions are extremely tedious to construct and often so long as to be hard to follow without assistance from a computer. Automated theorem proving is sometimes used to overcome these problems.

In general mathematical practice arguments are formal insofar as they are formalizable in theory; this is sometimes expressed by saying that mathematical arguments are rigorous. Mathematicians are happy to make a single inference that would, if formalized, amount to a long chain of inferences, because they are confident that the formal chain could be constructed if required.

Nevertheless, one advantage of formalizing arguments is the possibility of constructing a theory of valid mathematical arguments such as proof theory. Proof theory investigates the class of valid arguments in mathematics as a whole, and hence elucidates what kinds of statements can occur as conclusions to sound mathematical arguments. Gödel’s incompleteness theorems are proof-theoretic results which show the surprising fact that not all true mathematical statements can occur as the conclusion of formalized, sound mathematical arguments. In effect, not all true statements of mathematics are provable.

[edit] Logical arguments in science

In ordinary, philosophical and scientific argumentation abductive arguments and arguments by analogy are also commonly used. Arguments can be valid or invalid, although how arguments are determined to be in either of these two categories can often itself be an object of much discussion. Informally one should expect that a valid argument should be compelling in the sense that it is capable of convincing someone about the truth of the conclusion. However, such a criterion for validity is inadequate or even misleading since it depends more on the skill of the person constructing the argument to manipulate the person who is being convinced and less on the objective truth or undeniability of the argument itself.

Less subjective criteria for validity of arguments are often clearly desirable, and in some cases we should even expect an argument to be rigorous, that is, to adhere to precise rules of validity. This is the case for arguments used in mathematical proofs. Note that a rigorous proof does not have to be a formal proof.

In ordinary language, people refer to the logic of an argument or use terminology that suggests that an argument is based on inference rules of formal logic. Though arguments do use inferences that are indisputably purely logical (such as syllogisms), other kinds of inferences are almost always used in practical arguments. For example, arguments commonly deal with causality, probability and statistics or even specialized areas such as economics. In these cases, rather than to the well-defined principles of pure logic as explicitly set out and agreed upon in an academic, professional or other strictly understood context, logic in everyday usage almost always refers to something the reader or audience of the argument believe they perceive in the argument, and which drives them inexorably towards some conclusion, something perhaps ill-defined in their own minds (as opposed to putting the emphasis on examining by what criteria they actually accept this apparently compelling force as correct, which is how the formal rules of pure logic are constructed). And yet this feeling of inexorable conviction is also the foundation of those begrudgingly somewhat unsatisfying definitions we give of “logic”; in that we who are driven to construct these most conscientious, circumspect and clear definitions were initially drawn to do so by a similar belief that we recognized some intrinsic logic or compelling rational force in the world- even in the most everyday arguments, although such a view may have been naive, and is in any case incapable of being tested in any objective and/or universally satisfying fashion.

[edit] Theories of arguments

Theories of arguments are closely related to theories of informal logic. Ideally, a theory of argument should provide some mechanism for explaining validity of arguments.

One natural approach would follow the mathematical paradigm and attempt to define validity in terms of semantics of the assertions in the argument. Though such an approach is appealing in its simplicity, the obstacles to proceeding this way are very difficult for anything other than purely logical arguments. Among other problems, we need to interpret not only entire sentences, but also components of sentences, for example noun phrases such as The present value of government revenue for the next twelve years.

One major difficulty of pursuing this approach is that determining an appropriate semantic domain is not an easy task, raising numerous thorny ontological issues. It also raises the discouraging prospect of having to work out acceptable semantic theories before being able to say anything useful about understanding and evaluating arguments. For this reason the purely semantic approach is usually replaced with other approaches that are more easily applicable to practical discourse.

For arguments regarding topics such as probability, economics or physics, some of the semantic problems can be conveniently shoved under the rug if we can avail ourselves of a model of the phenomenon under discussion. In this case, we can establish a limited semantic interpretation using the terms of the model and the validity of the argument is reduced to that of the abstract model. This kind of reduction is used in the natural sciences generally, and would be particularly helpful in arguing about social issues if the parties can agree on a model. Unfortunately, this prior reduction seldom occurs, with the result that arguments about social policy rarely have a satisfactory resolution.

Another approach is to develop a theory of argument pragmatics, at least in certain cases where argument and social interaction are closely related. This is most useful when the goal of logical argument is to establish a mutually satisfactory resolution of a difference of opinion between individuals.

[edit] Argumentative dialogue

Arguments as discussed in the preceding paragraphs are static, such as one might find in a textbook or research article. They serve as a published record of justification for an assertion. Arguments can also be interactive, in which the proposer and the interlocutor have a more symmetrical relationship. The premises are discussed, as well the validity of the intermediate inferences. For example, consider the following exchange, illustrated by the No true Scotsman fallacy:

Argument: “No Scotsman puts sugar on his porridge.”
Reply: “But my friend Angus likes sugar with his porridge.”
Rebuttal: “Ah yes, but no true Scotsman puts sugar on his porridge.”

In this dialogue, the proposer first offers a premise, the premise is challenged by the interlocutor, and finally the proposer offers a modification of the premise. This exchange could be part of a larger discussion, for example a murder trial, in which the defendant is a Scotsman, and it had been established earlier that the murderer was eating sugared porridge when he or she committed the murder.

In argumentative dialogue, the rules of interaction may be negotiated by the parties to the dialogue, although in many cases the rules are already determined by social mores. In the most symmetrical case, argumentative dialogue can be regarded as a process of discovery more than one of justification of a conclusion. Ideally, the goal of argumentative dialogue is for participants to arrive jointly at a conclusion by mutually accepted inferences. In some cases however, the validity of the conclusion is secondary. For example; emotional outlet, scoring points with an audience, wearing down an opponent or lowering the sale price of an item may instead be the actual goals of the dialogue. Walton distinguishes several types of argumentative dialogue which illustrate these various goals:

  • Personal quarrel.
  • Forensic debate.
  • Persuasion dialogue.
  • Bargaining dialogue.
  • Action seeking dialogue.
  • Educational dialogue.

Van Eemeren and Grootendorst identify various stages of argumentative dialogue. These stages can be regarded as an argument protocol. In a somewhat loose interpretation, the stages are as follows:

  • Confrontation: Presentation of the problem, such as a debate question or a political disagreement
  • Opening: Agreement on rules, such as for example, how evidence is to be presented, which sources of facts are to be used, how to handle divergent interpretations, determination of closing conditions.
  • Argumentation: Application of logical principles according to the agreed-upon rules
  • Closing: This occurs when the termination conditions are met. Among these could be for example, a time limitation or the determination of an arbiter.

Van Eemeren and Grootendorst provide a detailed list of rules that must be applied at each stage of the protocol. Moreover, in the account of argumentation given by these authors, there are specified roles of protagonist and antagonist in the protocol which are determined by the conditions which set up the need for argument.

Many cases of argument are highly unsymmetrical, although in some sense they are dialogues. A particularly important case of this is political argument.

Much of the recent work on argument theory has considered argumentation as an integral part of language and perhaps the most important function of language (Grice, Searle, Austin, Popper). This tendency has removed argumentation theory away from the realm of pure formal logic.

One of the original contributors to this trend is the philosopher Chaim Perelman, who together with Lucie Olbrechts-Tyteca, introduced the French term La nouvelle rhetorique in 1958 to describe an approach to argument which is not reduced to application of formal rules of inference. Perelman’s view of argumentation is much closer to a juridical one, in which rules for presenting evidence and rebuttals play an important role. Though this would apparently invalidate semantic concepts of truth, this approach seems useful in situations in which the possibility of reasoning within some commonly accepted model does not exist or this possibility has broken down because of ideological conflict. Retaining the notion enunciated in the introduction to this article that logic usually refers to the structure of argument, we can regard the logic of rhetoric as a set of protocols for argumentation.

[edit] Other theories

In recent decades one of the more influential discussions of philosophical arguments is that by Nicholas Rescher in his book The Strife of Systems. Rescher models philosophical problems on what he calls aporia or an aporetic cluster: a set of statements, each of which has initial plausibility but which are jointly inconsistent. The only way to solve the problem, then, is to reject one of the statements. If this is correct, it constrains how philosophical arguments are formulated.

[edit] References

  • Robert Audi, Epistemology, Routledge, 1998. Particularly relevant is Chapter 6, which explores the relationship between knowledge, inference and argument.
  • J. L. Austin How to Do Things With Words, Oxford University Press, 1976.
  • H. P. Grice, Logic and Conversation in The Logic of Grammar, Dickenson, 1975.
  • Vincent F. Hendricks, Thought 2 Talk: A Crash Course in Reflection and Expression, New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8
  • R. A. DeMillo, R. J. Lipton and A. J. Perlis, Social Processes and Proofs of Theorems and Programs, Communications of the ACM, Vol. 22, No. 5, 1979. A classic article on the social process of acceptance of proofs in mathematics.
  • Yu. Manin, A Course in Mathematical Logic, Springer Verlag, 1977. A mathematical view of logic. This book is different from most books on mathematical logic in that it emphasizes the mathematics of logic, as opposed to the formal structure of logic.
  • Ch. Perelman and L. Olbrechts-Tyteca, The New Rhetoric, Notre Dame, 1970. This classic was originally published in French in 1958.
  • Henri Poincaré, Science and Hypothesis, Dover Publications, 1952
  • Frans van Eemeren and Rob Grootendorst, Speech Acts in Argumentative Discussions, Foris Publications, 1984.
  • K. R. Popper Objective Knowledge; An Evolutionary Approach, Oxford: Clarendon Press, 1972.
  • L. S. Stebbing, A Modern Introduction to Logic, Methuen and Co., 1948. An account of logic that covers the classic topics of logic and argument while carefully considering modern developments in logic.
  • Douglas Walton, Informal Logic: A Handbook for Critical Argumentation, Cambridge, 1998
  • Carlos Chesñevar, Ana Maguitman and Ronald Loui, Logical Models of Argument, ACM Computing Surveys, vol. 32, num. 4, pp.337-383, 2000.
  • T. Edward Damer. Attacking Faulty Reasoning, 5th Edition, Wadsworth, 2005. ISBN 0-534-60516-8

[edit] See also

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