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By Carol Hegarty

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K) Adding Connectives Using and , write logical forms for the sentences below. Note that (6) is ambiguous so there are two forms for it. Grammar A generates all and only well-formed formulae. Clive gave every child a biscuit or a Batman comic. Zoe read all the death notices but nothing else. There’s no business like show business. ) Chairman Miaou is heavier and meaner than any spaniel. Every prize was won by some high school kid. FURTHER READING Allwood, Andersson and Dahl’s (1977) Logic in Linguistics is an accessible introduction to first order logic and is particularly recommended.

5. The chief general difference between material implication and conditional sentences is that if is commonly not simply truth-functional in actual use. Given that material implication is truth-functional, the truth of an implication proposition depends only on a certain combination of truth values for the contained propositions, and the actual content or subject matter of those propositions is irrelevant. Logically, (18) expresses a perfectly fine (and true) implication, but it is odd as a conditional sentence.

Many theories analyse sentence meaning in terms of truth conditions, and such theories are called truth-conditional theories. Theories which analyse meaning in terms of referring to, denoting or describing things, situations and events in the world (or in possible worlds) are denotational theories. Most formal semantic theories are both denotational and truth-conditional. So far, the tools we have to analyse meaning are these: we have reality itself, also called the actual world, and all the infinitely many possible alternative ways reality might have been – these are the possible worlds (including the actual world).

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