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Propositional variables are the atomic formulas of propositional logic, and are often denoted using capital roman letters such as , and . [2] Example. In a given propositional logic, a formula can be defined as follows: Every propositional variable is a formula.
The predicate calculus goes a step further than the propositional calculus to an "analysis of the inner structure of propositions" [4] It breaks a simple sentence down into two parts (i) its subject (the object (singular or plural) of discourse) and (ii) a predicate (a verb or possibly verb-clause that asserts a quality or attribute of the object(s)).
PDL blends the ideas behind propositional logic and dynamic logic by adding actions while omitting data; hence the terms of PDL are actions and propositions. The TV example above is expressed in PDL whereas the next example involving := + is in first-order dynamic logic. PDL is to (first-order) dynamic logic as propositional logic is to first ...
Any variable is a term. Any constant symbol from the signature is a term; an expression of the form f(t 1,...,t n), where f is an n-ary function symbol, and t 1,...,t n are terms, is again a term. The next step is to define the atomic formulas. If t 1 and t 2 are terms then t 1 =t 2 is an atomic formula
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
Notes on games in temporal logic by Ian Hodkinson, including a formal description of first-order temporal logic; CADP – provides generic model checkers for various temporal logic; PAT is a powerful free model checker, LTL checker, simulator and refinement checker for CSP and its extensions (with shared variable, arrays, wide range of fairness).
It is notable that while we have variables for predicates in second-order-logic, we don't have variables for properties of predicates. We cannot say, for example, that there is a property Shape(P) that is true for the predicates P Cube, Tet, and Dodec. This would require third-order logic. [2]
[2] Lewis used the notion of propositional functions to introduce relations, for example, a propositional function of n variables is a relation of arity n. The case of n = 2 corresponds to binary relations, of which there are homogeneous relations (both variables from the same set) and heterogeneous relations.