By Emmon Bach
This e-book is an creation to the present advancements in model-theoretic semantics, which has turn into an important a part of the paintings in theoretical linguistics over the past decade. the writer examines the version constitution of Montague’s thought after which offers gildings in this easy version which have been of specific significance within the previous few years: generalized quantifiers, the creation of extra constitution within the area of people, houses as primitive components within the version, events and comparable ’smaller’ global like entities. not anything is presupposed approximately wisdom of the mathematical and logical instruments utilized in formal semantics, and Bach provides the casual with at the very least formalism.
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Additional resources for Informal Lectures on Formal Semantics
Here is the new rule: R8. If F is a formula and x is a variable, then LAMBDA x [F] is a predicate. S8. LAMBDA x [F](a) is true on an assignment g iff for all assignments g' that differ from g at most in their assignment of a value to x and such that g'(x) is the individual denoted by a, F is true. I regret that I have to say that in such a complicated way. Let me give a few examples to clarify my meaning: 8. LAMBDA x [Run(x)](a) is true iff the individual denoted by a, say Anne, runs. < previous page page_38 If you like this book, buy it!
Next page > < previous page page_38 next page > Page 38 R7. If F and G are formulas, so is (F ® G). S7. (F ® G) is true iff F is false or G is true. (From example S7 you can see that we can state the truth conditions for the formulas constructed with in terms of negation and disjunction, that is, not and or. This relation is sometimes called material implication to emphasize that it is a technical concept and does not correspond exactly to the way we use if ... ) We will need this relation in order to see how to deal with the denotations of some noun phrases like every fish.
Now, if there is one thing that I believe about universals in syntax, it is that all languages, no matter how different their structures, have a type of constituent or category that we call noun phrase, and further I believe that in all languages this category includes not just things like names or pronouns (as in PC) but also expressions such as three fish, every child, and some tiger. (I do not mean that the internal structure of such noun phrases is constant across languages. ) If the logicians' languages such as PC are supposed to be getting at the heart of the logical structure of language, wouldn't it be strange that natural languages show such a very different way of expressing things such as examples 2 and 13?