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Elements of Formal Semantics This chapter introduces some of the key notions about the analysis of meaning in formal semantics. We focus on entailments: relations between premises and valid conclusions expressed as natural language sentences. Robust intuitions about entailment are distinguished from weaker types of reasoning with language. Speaker judgments on entailments are described using models: abstract mathematical structures, which emanate from semantic analyses of artificial logical languages. Model-theoretical objects are directly connected to syntactic structures by applying a general principle of compositionality.We see how this principle helps to analyze cases of structural ambiguity and to distinguish them from other cases of under-specification.
What do dictionaries mean when they tell us that semantics is “the study of meaning”? The concept that people intuitively refer to as “meaning” is an abstraction inspired by observing how we use language in everyday situations. However, we use language for many different purposes, and those various usages may inspire conceptions of meaning that are radically different from one another. We cannot reasonably expect a theory of meaning to cover everything that people do with their languages. A more tractable way of studying meaning is by discerning specific properties of language use that are amenable to scientific investigation. These aspects of language use, if stable across speakers and situations, will ultimately guide us toward a theory of language “meaning”.
ENTAILMENT
One of the most important usages of natural language is for everyday reasoning. For example, let us consider sentence (2.1):
(2.1) Tina is tall and thin.
From this sentence, any English speaker is able to draw the conclusion in (2.2) below:
(2.2) Tina is thin.
Thus, any speaker who considers sentence (2.1) to be true, will consider sentence (2.2) to be true as well. We say that sentence (2.1) entails (2.2), and denote it (2.1)⇒(2.2). Sentence (2.1) is called the premise, or antecedent, of the entailment. Sentence (2.2) is called the conclusion, or consequent.
The entailment from (2.1) to (2.2) exemplifies a relation that all English speakers will agree on. This consistency is remarkable, and all the more so since words like Tina, tall and thin are notoriously flexible in the way that they are used.
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