Semantic Theories (Fach) / Formal Semantics (Lektion)
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- It is characteristic of formal semantics.. to first develop a formal and explicit semantic representation of the meanings of words, phrases and sentences and then to define a translation between syntactic and semantic structures -> R. Montague
- Montague's approach is: A semantic theory must characterise the relationship that exists between lnguistic expressions and the things to which they relate -> formal semantics is a theory of reference -> quite unlike the view held by Katz and Fodor
- Formal semantics makes the following assumptions words and sentences are the carriers of meaning theory must derive the meanings of larger units from those of smaller units construction of meaning is rule governed in the same way that the construction of the well formed syntactic expressions of a language is rule governed -> for each syntactic rule there is a corresponding semantic rule systematic meaning relations that hold between different sentences / words of a language truth conditions are relevant -> formal semantics is a correspondence theory of truth, claiming that a statement in some language is true if it corresponds to some state of affairs
- What we know if we know the meaning of the sentence "The book is on the table" is: conditions that must obtain for the sentence to be true core meaning of a sentence is its truth conditions core meaning of a sentence as a statement is to understand the conditions under which it could be true - formal semantics uses a specific metalanguage->precisely defined (no ambiguities) -> similar to mathematics or logic
- Why it is necessary to make use of a metalanguage? formal semantics is explicit, in a formal system it is possible to prove that semantics is without contradictions and complete in order to understand how formal semantics works, we must first understand the metalanguage or formal language that it uses
- What does the metalanguage of formal semantic systems look like? metalanguage and the construction of formal semantic systems are built upon and draw from truth-functional logic, predicate logic and set theory
- What is truth-functional logic? makes uses of the following constituents: sentence variables: p,q ; sentence connectors: &, ^ etc with these constituents truth-functional formulae are established. aim: to evaluate the truth values of sequences of sentences (contents are of no interest). complex argumentation can be checked for tautologies, contradictions or inconsistencies. in order to derive the truth value of complex formulae there are truth-value conditions for sentence connectors which are also represented in tables of truth values
- The truth-value conditions are conjunction: and (&) p & q is true, if both sentences are true, otherwise false disjunction: or (v) p v q is true, if at least one of the sentences is true, otherwise false implication: if, then (->) p -> q is only false, if the antecedent is true and the consequent is false negation: not -p is true if p is false, and false if p is true
- whether the formula contains a tautology or a contradiction has to be computed.. in formal semantics, in many cases the computing of truth values is not relevant because the aims are different
- Predicate logic the contents of sentences are considered a logic of declarative sentences based on truth-functional logic: all connectors the same, in addition operators are introduced. sentence variables don't occur because sentences are analysed
- predicate logic makes use of the following constituents individual constants: smll letters predicate constants: capital letters individual variables: x, y, z quantifiers: 1. existential E, 2. universal A, 3. iota 1 predicates are assumed to be functors! number of their arguments conforms to their arity: John smokes S(j) John saw Susan: S(j,s) in a formula, every variable must be bound by a quantifier: John read a story: E x [S(x) & R(j,x)] variables represents individuals
- Nominal complex descriptions like "a good story" are split up into their semantic constituents and combined by a sentence connector are considered as a unit, alway occur on the same side of an implication complex predicates modified by adverbs are described as predicates over predicates: John ran fast R(j) & F (R(j)) Every new car is very good Ax [(C(x) & N(x)) -> V(G(x))]