Sentence examples for predicate logic for from inspiring English sources

1.4, for a proof that there does not exist a semantics assigning individuals or sets of individuals even to phrases of the two forms all A and some B in a systematic (compositional) way. 5. Some such properties were considered even in the early days of predicate logic, for example, the quantifier ∃! meaning 'there exists exactly one.' (see section 6 for the notation on the right-hand side).

The mined rules are translated into predicate logic for further verification of correctness.

Liberate yourself from any gods, messiahs, prophets, and spiritual teachers by deciding to believe only what survives rigorous scientific proof (or predicate logic, for those with a mathematical bent), based on axioms that are acceptable to you; then question your axioms, and repeat.

Such variable functors act like the predicates of first-order predicate logic except for taking propositional rather than nominal arguments.

By 1928, in Hilbert and Ackermann's Grundzüge der theoretischen Logik, an axiomatic formal system for predicate logic was presented, together with the problem of its completeness.

The fourth foundational problem, the decision problem for predicate logic, was shown to have a negative solution in a short paper by Church in 1936 as a corollary to Gödel's incompleteness theorem.

It is clear that there was a good understanding of the principles of predicate logic in this tradition, for how could there have been a Löwenheim-Skolem theorem otherwise?

(Examples from logic are Turing's famous halting function (described in the entry on Turing machines) and the function D whose domain is the set of well-formed formulae of the predicate calculus and whose values, D x), are 1 or 0 according to whether x is, or is not, derivable from the Bernays-Hilbert-Ackermann axioms for predicate logic).

This is done by using a theorem prover for predicate logic which by a refutation method checks if this set is inconsistent or not.

Troelstra's [1998] presents formulas-as-types and (Kleene and Aczel) slash interpretations for propositional and predicate logic, as well as abstract and concrete realizabilities for a multitude of applications.

The level of knowledge of logic expected for exemption, or tested on the examination, is what is covered in Logic I at MIT: proof procedure and semantics for first-order predicate logic with identity, and some acquaintance with standard metalogical results (for example, those concerning completeness, incompleteness and decidability).