Introduction to Formal Semantics

Introduction to Formal Semantics

1. MEANINGS AND DENOTATIONS

   • Semanticists
     • They focus on theories of meaning that apply to statements that make statements and are considered true or false
   • The assumption
     • Provides a paradigm of the type of relationship between linguistic expressions and world that is at the center of linguistic meaning
   • Addition assumption
     • Declarative sentences used to make statements such as interrogatives used to ask questions and the imperatives they communicate commands

2. SYNTACTIC CATEGORIES

   • The main syntactic categories which Frege identifies in natural language correspond to the types of first-order logic.
     • Individual terms
       • names of individuals, and variables that occur in the same positions in sentences that names do
     • Predicates
       • terms for properties and relations
     • Connectives
       • (and, or, if, then, and not
     • quantifiers that are linked to variables
       • bind the variables

3. In addition to the Frege-Carnap view there is another approach, which dispenses with intensions and seeks to construct a theory of meaning solely in terms of the contributions which expressions make to the truth condition of sentence

   • This approach is developed by Davidson
     • it takes as its starting point Tarski's (1933) definition of truth for first-order languages.
       • Tarski constructs a recursive definition of the predicate irue-in-L for a class of first-order languages similar to the first-order language characterized by Frege
       • Tarski constructs a recursive definition of the predicate irue-in-L for a class of first-order languages similar to the first-order language characterized by Frege
         • Davidson regards Tarski's truth definition as the paradigm of a semantic theory

4. DYNAMIC SEMANTICS: BEYOND STATIC SENTENCE MEANING

   • This perspective allows us to focus on the way in which the meanings of a sentence's constituents contribute to its truth conditions
     • we generally encounter a sentence as a part of a discourse, where we understand it on the basis of preceding contributions to the conversation.
       • When we situate sentence meanings in a discourse, they are no longer static objects, but active devices that have the capacity to inherit semantic content from previous sentences, modify it, and pass on the new information to the next sentence in the sequence.

5. MEANING AND SITUATIONS: BEYOND POSSIBLE WORLDS

   • A world is the result of assigning the objects of a domain to properties and relations in such a way as to produce a complete state of affairs containing these objects.
     • There are at least some cases where it seems to be neccesary to use situations rather than worlds to specify the interpretation of a sentence
       • A situation is smaller and more fine-grained object than a entire world
         • it can be contained in larger situations, and it is, in effect, the specification of part of a word (equivalently, a partial specification of a world).

6. UNDERSPECIFIED REPRESENTATIONS: BEYOND COMPOSITIONALITY

   • Montague grammar satisfies the condition of compositionality by characterizing the relation between the set of syntactic categories and the set of semantic types as a homomorphism which maps each syntactic structure into a single denotational type.
     • " In this framework the meaning of an expression is fully determined by (a) its syntactic structure and (b) the meanings of its constituents".
   • the condition of compositionality requires that the meaning of any expression P be computable by a function which, given the meanings of P's syntactic constituents as its arguments, yields P's meaning as its value.

7. JIMENA CRUZ CRUZ