## The New Encyclopaedia Britannica, Volume 11Encyclopaedia Britannica, 1983 - Encyclopedias and dictionaries |

### From inside the book

Results 1-3 of 30

Page 45

Natural deduction rules have also been formulated for some other branches of

logic mentioned in this article — e.g., for the lower

various systems of modal logic (IV. Alternative systems of modal logic). HI.

Natural deduction rules have also been formulated for some other branches of

logic mentioned in this article — e.g., for the lower

**predicate**calculus (III.) and forvarious systems of modal logic (IV. Alternative systems of modal logic). HI.

Page 48

Rules of uniform substitution for

very complicated; and, to avoid the necessity for these rules, axioms for these

systems are therefore usually given by axiom schemata in the sense explained in

II.

Rules of uniform substitution for

**predicate**calculi, though formulable, are mostlyvery complicated; and, to avoid the necessity for these rules, axioms for these

systems are therefore usually given by axiom schemata in the sense explained in

II.

Page 1083

It is then easy to use the usual rules of the

statement, "There exists an x such that, for every y, x is not M of y"; i.e., ( 3 x ) ( Vy

) ~Mxy. In other words, the negation of (3) is a theorem of the

It is then easy to use the usual rules of the

**predicate**calculus to derive also thestatement, "There exists an x such that, for every y, x is not M of y"; i.e., ( 3 x ) ( Vy

) ~Mxy. In other words, the negation of (3) is a theorem of the

**predicate**calculus.### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

19th century army atoms axiomatic axioms bearings became BIBLIOGRAPHY body centre century church coil dipoles Dutch economic electric electrons energy example ferromagnetic Figure fluid flux density force France French friction function gears German helium-3 Holland important industry King known land later Lo-yang load lock locomotion loess logic logicians logistic London Louis Low Countries lubricant luminescence Luther Lutheran Luxembourg lymph lymph nodes lymphatic Macau machines Mackenzie River Madagascar Madhya Pradesh magic magnesium magnetic field material mechanical ment Merina metal metalogic metre miles modal modal logic motion move movement Netherlands nodes nuclear operations particles percent political population predicate produced propositions provinces river rotation rule screw shaft speed square square miles stadholder surface syllogisms temperature theorem theory tion torque towns trans types United valid variables velocity wff's