Re: Sensible and NonsenSQL Aspects of the NoSQL Hoopla
Date: Mon, 23 Sep 2013 15:27:04 -0700 (PDT)
Message-ID: <1ec5e237-6380-4aed-b5af-06a6a119e304_at_googlegroups.com>
Dana srijeda, 4. rujna 2013. 18:35:36 UTC+2, korisnik Jan Hidders napisao je:
> On 2013-09-03 19:46:22 +0000, Eric said:
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> Codd explicitly referred to first-order logic in his work, so the link
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> with Frege was clearly made.
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> -- Jan Hidders
Gottlob Frege is a scientist, who in the last ten years, emerges to the surface as a scientist of great importance. Lately, more and more scientists reveals its importance in mathematics, philosophy and other sciences. Some of the most famous scientists proclaim him as the greatest mathematician and philosopher, so far. Here I will briefly mention his work, which determines the relational model as a semantic model:
- The theory of language.
- The formalization of spoken languages
- Formal languages for Propositional Logic and FOL
- Semantics. This part is actually completely new in the history of science and has strong influence on the work of A. Tarski (Model Theory) and R. Montague. (The formalization (syntax and semantic) of spoken languages.)
- Philosophy of language - introduces a whole new realm of philosophy.
- Complete construction of the Propositional logic
- Formalization of Propositional Logic
- Frege introduces the following algorithm: the truth-value of a proposition is determined by its form and the truth-values of its atomic constituents. Here the form is a complex proposition which joins its atomic propositions using the five logical connectives. The constituents are atomic propositions.
Note that Frege defined that the meaning of a sentence is its truth value. In this way he connected logic and semantic at the level of sentences. Frege was the first who begin to develop a technique for the proof theory. He was representing propositions as trees. As far as I know, Wittgenstein introduced truth-tables. However, as I already mentioned Frege introduced the algorithm for the complex propositions; he was using trees. Note that there is no a proof for truth-tables.
3) Frege developed completely FOL. He introduced formal language for FOL and he developed philosophy for spoken languages. I will mention only the part which is related to Predicate Calculus. I will briefly described Frege’s ideas that are related to sentences, names and predicates. I already mentioned that the meaning of a sentence is its truth value. The meaning of names was elaborated in Frege’s deep theory about names. This theory has changed many things in science. So if somebody says that E. Codd was the first who introduced the new representation of the relations by using names, then it is the false sentence. Even more, it seems to me that this claim implies that E. Codd in fact introduced relationships between names and predicates.
I will explain that this is a part of Frege’s theory. Frege introduces the following:
(i) Saturated expressions;
Here we have grammatical categories Names, (N is shortcuts for a name) and
Sentences (S is shortcuts for a sentence)
(ii) Unsaturated expressions
There are many types of unsaturated expressions, which have one or more “gaps”.
If the gaps were filled in with an expressions and if they produce expressions of type S then these unsaturated expressions we call predicates.
The notation that is suitable for a formal work with these gaps and with other Frege’s ideas can be represented with the following scheme:
(1) S/N, S/NN, S/NNN , … This kind of types Frege called relations.
(2) Second-level, predicates
S/(S/N), S/(S/N)(S/N), S/(S/N)(S/N)(S/N).….
(3) Third-level predicates
S/(S(S/N)),….
……etc
Of course, in this representation, there are cross-combinations. What is important here for the Relational model is the case (1). The types from case (1), Frege called relations, and case (1) completely defines the relational model as a semantic model.
Definition of predicate: A predicate, in a spoken language, is an incomplete phrase with specified gaps such that when gaps filled with names of entities the phrase becomes a proposition.
In the relational model, we do not use the gaps, but the names (of attributes). Now we can introduce atomic predicates by using atomic propositions. The conjunction of atomic propositions is commutative. From this fact follows that the relation can be represented by the names of the attributes and order of attributes (columns) is irrelevant.
Above written notation was done by Polish mathematician K. Ajdukiewicz. This is a formalization of Frege's theory of linguistic structures - the part that refers to the predicate, sentences and names and its logic and semantic laws. This issue of the names and predicates is important also because it is part of a more general theory given by Frege. Note that philosophy is divided on two huge parts: the realm of the external world and the realm of the purely mental. Today it is clear that Frege introduced the third realm, that is, the realm of semantics that connects two mentioned realms. Therefore, the claim that E. Codd first introduced relations, whose values refer to corresponding names of attributes, reaches far into the substance of the Frege's theory. With regard to what is shown above in this post, it is clear that the claim that E. Codd first introduced representation of relations, using the name of the attributes is not correct. Note that the claim about "Codd's Relations" can be found (even) in some textbooks, which are at university level?!
Mentioned notation was used by the Polish mathematician Ajdukiewicz for Categorical grammar (in 1935). Montague grammar (syntax) also used Categorical grammar. I write about this in order to emphasize the importance, the power and influence of Frege's work.
Note that the semantic here(in RM) is realized just by using the language constructs. For example, in my data model the semantic is based on concepts.
There are also questions about (maybe) some limitations of predicate logic related to formalization of the corresponding propositions? For example for tensed propositions.
Vladimir Odrljin Received on Tue Sep 24 2013 - 00:27:04 CEST