The formal language studied in this paper contains two categories of expressions, terms and formulas. Terms express events, formulas propositions. There are infinitely many atomic terms and complex terms are made up by Boolean operations. Where α and β are terms the atomic formulas have the form α=β (α is the same as β), Forb α (α is forbidden) and Perm α (α is permitted). The formulae are truth functional combinations of these. An algebraic and a model theoretic account of validity are given and an axiomatic system is provided for which they are characteristic.
The ‘closure principle’, that what is not forbidden is permitted is shown to hold at the level of outcomes but not at the level of events. In the two final sections some other operators are considered and a semantics in terms of action games.
KeywordsMathematical Logic Final Section Boolean Operation Formal Language Computational Linguistic
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