Semantics I acknowledgements
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| 3.4.4 Predicate Logic As we have seen that propositional logic or prepositional calculus deals with relations between sentences, predicate logic deals with relations among predicates. In propositional logic, the relations are between sentences (within two sentences, while in predicate logic the relations are among predicates (more than two sentences. But they are not wholly different, as predicate logic is included in proposition or sentence or in the predicate logic we deal also with relation among sentences. Let’s seethe examples All animals are animate. - Dogs are animal. - Therefore dogs are animate. The predicate of the first proposition is are animate that is, what is said about the property of the animals, it is symbolized with A, the subject (what the preposition is about) is symbolized with x, where x refers to any individual or it is variable which substitutes any individual, the same with y and z. if the subject is a specific individual like John, Mary, or Brown as the name of dog, the symbol will be ab, and c. these symbols are called individual constants. The symbol A here is the initial of animals, so it is not a conventional symbol. SEMANTICS Page In our example above we find the quantifier all which indicates any animal, both individual animal, so we substitute symbol x for this, whereas the quantifier all is symbolized with V. thus the predicate calculus of the proposition would be V x (AX) C (x) We read it : For all x, s, if x s are animal, x s are animate. The symbol C stands for animate. The example can also be put like this V x ( A (x) C (x) A (a) C (a) In this case the subject is a specific one. After analyzing the predicate logic, we can now understand that it is the argument that has relation of predicate with the proposition. Beside their relation within proposition, what is then the elements of predicate Do the term predicate and predication have the same interpretation These will be discussed in chapter four, in the Predicate Analysis. Up to this point we have discussed about the logic and its extensions, our problems now is, is it the same logic to logicians with logic to linguists As what is seen in simple example of the use of neither…… nor….., where not XX is any proposition) for logicians the proposition John is not a man is an abbreviation for John is neither a manor nor is he SEMANTICS Page 52 a man, because it has the same truth value. Whereas for linguists it is not well formed. Then it should be : John is neither a man nor a woman. For in using neither….nor…., the non it follows cannot be the same. If he is neither a man nor a woman, what is he? |