Theories of Semantics on theWeb - Social Semantics: The Search for Meaning on the Web - page 91

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Fig. 4.1 Models, entailment, and inference

expression” in the language (Hayes 2004). While again the history and debate over
these terms is outside the scope of this thesis, in general the original notion, as
pioneered by Carnap (1947), is that a certain kind of thing may only be described ,
and so given an intension , while the things that satisfy this description (which
may be more than one thing) are extensions . Sentences are consistent if they can
be satisfied ,theyare inconsistent if otherwise. Lastly, note that an entailment
is where an interpretation of one sentence to some content always satisfies the
interpretation of another sentence to some content , i.e. the first statement entails
the second. In contrast, an inference is a syntactic relationship where one sentence
can be used to construct another sentence in a language . In detail, as shown
in Fig. 4.1 , the syntactic inference mechanisms over time produce more valid
inferences, and because these inferences 'line up' with entailments, they also may
accurately describe the world outside the formal system. Ideally, this model also
'lines-up' with the world, so the inferences give one more correct statements
about the world. Models can be captured in various ways. We have primarily
described a denotational semantics, but often axiomatic and operational semantics
are equally powerful formalisms. Inference can usually be accomplished by some
local inference procedure, like a computer program. The inference procedure of
a language is sound if every inferred sentence can be satisfied (i.e. the inference
mechanism preserves 'truth'), and it is complete if every satisfied sentence can be
shown to be entailed (i.e. all 'true' statements can be proven). This is necessarily
a quick overview of the large field of formal semantics, but the general notions are
illustrated in Fig. 4.1 as the parallel between the causal relationships of the syntactic
sentences and their interpretations to a model that semantically refers to the world.