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...ath>Q</math> is said to be a tautological consequence of one or more other propositions (<math>P_1</math>, <math>P_2</math>, ..., <math>P_n</math>) in a [[formal p ...if and only if in every row of a joint truth table that assigns "T" to all propositions (<math>P_1</math>, <math>P_2</math>, ..., <math>P_n</math>) the truth table ...

...ormula#An algebra of propositions.2C the propositional calculus|algebra of propositions]], [[Material conditional|material implication]]; in the two-element algebr ...

...=119807724|issn=0003-9519}}</ref> is a [[treatise]] that consists of three propositions, probably made by [[Archimedes]], ca. 250 BCE.<ref>{{Cite journal|last=Lit| ==Propositions== ...

Inquisitive propositions encode informational content via the region of logical space that their inf ...th>P\cap Q</math> and <math>P \cup Q</math> respectively. Thus inquisitive propositions can be assigned to formulas of <math>\mathcal{L}</math> as shown below. ...

...this role may be played by the number ''7''. Below, ''φ'' and ''ψ'' denote propositions not depending on ''x'', while ''θ'' is a predicate that can depend on in. .../math>. The schema implies the strictly weaker excluded middle for negated propositions (WLEM) through the intuitionistic form of [[consequentia mirabilis]]. ...

..."atomic propositions". That is, the property contains sequences of sets of propositions, each sequence known as a "word". Every property can be rewritten as "''P'' ...such as <math>w:=\{a\}\{a,b\}\empty \{a,b\}^\omega</math> (for the atomic propositions <math>AP=\{a,b\}</math>). A linear time (LT) property over ''AP'' is a subs ...

where <math>A</math> and <math>B</math> are any propositions. Most constructive logics only reject the former, the law of excluded middl for any two propositions. For <math>B</math> taken as the contradiction <math>A\land \neg A</math> i ...

...ifth icon'' is required for the principle of [[excluded middle]] and other propositions connected with it. One of the simplest formulae of this kind is: ..., not even the constraint <math>\neg Q\to P</math> implies the law for two propositions. Postulating the latter to be valid results in [[Intermediate logic#Propert ...

...t1=Zhegalkin |first1=Ivan Ivanovich |title=On the technique of calculating propositions in symbolic logic|journal=Matematicheskii Sbornik |date=1927 |volume=34 |is ...

...1769 |issn=1432-0657}}</ref> The second book, which contains ten [[Theorem|propositions]], examines the centres of gravity of [[Parabola|parabolic]] segments.<ref ...the Equilibrium of Planes'' I, which contains seven postulates and fifteen propositions, uses the centre of gravity for both commensurable and incommensurable magn ...

...to line numbers, preferring instead to either give full lists of precedent propositions or alternatively indicate the left-hand sides by bars running down the left ...I" justifies P∧Q. The assumptions are the collective pool of the conjoined propositions. ...

...s. Klee's added chapter, lying between the two halves, provides another 10 propositions, including some generalizations to higher dimensions, and the book conclude ...

where <math>P</math>, and <math>Q</math> are propositions expressed in some [[formal system]]. ...

...choice function on all sets of this form, implies excluded middle for all propositions. ...umbers form a set one may quantify over), then set-bounded but undecidable propositions can be expressed. ...

...do), it will make no difference: the outcome is already settled. Thus, if propositions bear their truth-values timelessly (or unchangingly and eternally), then pl ...

...the number of compound propositions that can be made from only ten simple propositions exceeds a million. (Hipparchus, to be sure, refuted this by showing that on ...d that the number of compound propositions that can be made from 10 simple propositions exceeds a million. Contemporary philosopher {{harvs|first=Susanne|last=Bob ...

Claims made by any of the propositions ("the next statement is not true") stand in contradiction with an implicati ...ftrightarrow \neg P</math>. So no consistent theory proves that one of its propositions equivalent to itself. Metalogically, it means any axiom of the form of such ...

|title=The Undecidable – Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions |title=On undecidable propositions of formal mathematical systems ...