# logical axiom in a sentence

1) Thus non-

**logical**

**axioms**, unlike

**logical**

**axioms**, are not "tautologies".

2) We fix some axiomatization of the predicate calculus:

**logical**

**axioms**and rules of inference.

axiom collocations

3) Typical Hilbert-style systems have a small number of rules of inference, along with several infinite schemes of

**logical**

**axioms**.

4) The

**logical**

**axioms**consist of several

**axiom**schemes of logically valid formulas; these encompass a significant amount of propositional logic.

## logical axiom example sentences

5) Aristotle referred to such commonly held beliefs not as "koinai doxai", which is a term he used for self-evident**logical**

**axioms**, but with other terms such as "endoxa".

6) Researchers match missions to the capabilities of available resources, defining ontology as "a set of

**logical**

**axioms**designed to account for the intended meaning of a vocabulary.

7) This is the operator associating any set "X" of formulas with the set "J(X)" of formulas which are either

**logical**

**axioms**or are obtained by an inference rule from formulas in "X" or are in "X".

8) A deductive system for a logic is a set of inference rules and

**logical**

**axioms**that determine which sequences of formulas constitute valid proofs.

9) According to Carnap's "Logicist Foundations of Mathematics", Russell wanted a theory that could plausibly be said to derive all of mathematics from purely

**logical**

**axioms**.

10) One seemingly peculiar, but within the overall framework strictly logical,

**axiom**of Luhmann's theory is the human being's position outside any social system, initially developed by Parsons.

11) However, natural deduction systems have no

**logical**

**axioms**; they compensate by adding additional rules of inference that can be used to manipulate the

**logical**connectives in formulas in the proof.

12) A deductive system consists of a set __FORMULA__ of

**logical**

**axioms**, a set __FORMULA__ of non-

**logical**

**axioms**, and a set __FORMULA__ of "rules of inference".

13) These

**axiom**schemata are also used in the predicate calculus, but additional

**logical**

**axioms**are needed to include a quantifier in the calculus.

14) In mathematics, the term

**axiom**is used in two related but distinguishable senses : "

**logical**

**axioms**" and "non-

**logical**

**axioms**" .

### example sentences with axiom

15) ' There are at least six**logical**

**axioms**or principles that show what people mean whenever they make statements about 'necessity' or 'possibility' (described below).

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