Sentence examples for truth of a formula from inspiring English sources
Truth of a formula is given with respect to a point.
Informally speaking, when the usual procedure of determining classical truth of a formula is applied to tr\((F \), it will test the provability (not the truth) of each of \(F\)'s subformulas, in agreement with Brouwer's ideas.
In the case of propositional logic, when discussing the truth of a formula A, any relevant model can be specified in terms of propositional formulas, namely literals (positive or negative atomic formulas).
The truth of a formula of TL at a given time instant \(t\) in a given temporal model \(\mathcal{M}\) is defined inductively as follows: A formula \(\varphi\) of TL is valid, denoted \(\models \varphi,\) if it is true at all time instants in all temporal models; a formula \(\varphi\) is satisfiable if it is true at some time instant in some temporal model.
Now, the definition of (Ockhamist) truth of a formula of OBTL in \(\mathcal{M},\) relative to a branch \((h,t)\) where \(h \in \mathcal{H}\) and \(t\in h\), is given recursively as follows: We now say that a formula of OBTL is Ockhamist valid if it is true on every branch of every Ockhamist tree model.
By the definition of truth for a formula □B, □p is false in all the worlds of the maximal model, and ◊p is true in all of them.
Another benefit of the connection calculus is the independence of a truth value of a formula, represented by a matrix, from some operations performed on matrices, which in particular correspond to commutativity of conjunction and disjunction symbols.
In the standard model theory for second-order quantification, we explain the truth conditions of a formula of the form $\forall X \ A$ in terms of ordinary quantification over sets.
The former tell us that the truth of a disjunctive formula is determined by the truth of one or other of its disjuncts, whilst the truth of a conjunctive formula is determined by the truth of both its conjuncts.
The point is that to determine the truth-value of a formula without modals at a Leibnizian time defined as t = temp(m,c), one need not look at other chronicles than c if the evaluation is going to take place on the basis of Leibnizian semantics.
A fundamental concern about the semantical treatment of vague predicates is whether an adequate semantics should be truth-functional, that is, whether the truth value of a complex formula should depend functionally on the truth values of its subformulas.
