Sentence examples for first order valuation from inspiring English sources

A first order valuation \(w\) is an \(x\ -variant of valuation \(v\) if \(v\) and \(w\) agree on all variables ex\ -variantbly fof \(x\).

Truth, at a state \ \Gamma\) of a model \ \cM = \langle \bG, \bR, \bD_{O}, \bI\rangle\), with respect to a first order valuation \ v\), is characterized as follows, where \(P(x_{1}, \ldots,x_{n})\) is an atomic formula: Call a formula valid if it is true at every state of every first order model with respect to every first-order valuation, as defined above.

A first-order valuation in a model is a mapping \ v\) that assigns a member of \ \bD_{O}\) to each variable.

A first-order valuation in FOIL model \ \cM\) is a mapping that assigns to each object variable a member of \ \bD_{O}\), as before, and to each intension variable a member of \ \bD_{i}\).

First order of business: bathrooms.

The first order, he said, "worked out.

results in (first order) Peano Arithmetic (PA).

The first order of business?

The fictional group is the "First Order".

For example we define classical propositional consequence by means of truth valuations, first-order consequence relation by means of structures, the intuitionistic consequence relation by means of Kripke models, etc.

Hence a part of the specification of an alethic dialogue in the case of propositional logic will be a valuation function, and in the case of first-order logic a τ-structure for an appropriate vocabulary τ.