Sentence examples for given a logic from inspiring English sources

Given a logic L, a logical matrix < A, D > is said to be a model of L if wherever Γ ⊢L φ then every valuation v on A that maps the elements of Γ to some designated value (i.e. an element of D) also maps φ to a designated value.

The idea of the decomposition is quite natural: given a logic L, presented as a pair L = ⟨C, ⊢L⟩ in which C is a signature and ⊢L is a consequence relation, a family of translations f i : L(C) → L(Ci) (for i ∈ I) is taken into consideration.

Given a logic \(\mathcal{L}\) specified in this manner, we may now formulate the following problems: \(\sc{SATISFIABILITY}_{\mathcal{L}}\ \) Given a formula \ \phi \in \text{Form}_{\mathcal{L}}\), does there exist a structure \(\mathcal{A} \in \mathfrak{A}\) such that \(\mathcal{A} \models_{\mathcal{L}} \phi\)?

Her husband, Jacques Putman, a wealthy art critic, collector and publisher, introduced her to contemporary art and the world of Modernism, which gave a logic and confidence to her instinctively Modernist voice.

In idle state, the proposed controller gives a logic high signal through the MOSI line and it also receives a logic high signal from the SDHC card.

We then give a logic programming implementation of our algorithm and use it to give a standard procedural algorithm, and analyze the complexity of constructing k-maintainable controls, under different assumptions such as k= 1, and states described by variables.

The properties of the corresponding biotic network show to what extent a given vector is exploiting its potential food sources, evolutionary dynamics giving a logic as to why this usage should be optimal.

He might also become overly confident and simply laugh her off every time she gives a logic-challenged answer to a question.

Given a normal logic program, we show that by adding, for each loop in the program, a corresponding loop formula to the program's completion, we obtain a one-to-one correspondence between the answer sets of the program and the models of the resulting propositional theory.

(Think of trying to give a logical argument for trusting logic, or basic inference patterns like modus ponens).[1] That problem doesn't go away just because most people will accept certain principles.

Given a mixed-logic dynamical system, we derive an explicit controller in the form of a possibly discontinuous piecewise-affine function.