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If P tautologically implies Q, then when P is true Q must be true. It can never
happen that P is true and Q false, since it is required that P —> Q he a tsutology.
Thus from the premise P we may safely infer Q without recoulse to any other
premises ...
2
Logic, Sets, and Recursion
0 is tautologically consistent with F iff FU{ 0 } is satisfiable. 0 is tautologically
independent of F iff 0 is not a tautological consequence of F. Suppose that -></>
is not a tautological consequence of F, so there is an interpretation I that satisfies
F, ...
3
An Introduction to Formal Logic
First, let's giveaformaldefinition: The PLwffs A 1,A2,..., An tautologically
entailthewffCifand only if there is no valuation of the atoms involved in the
AiandC which makes A 1 , A 2 , ..., A n simultaneously all true and yet C false. If a
bunch of ...
4
Sets, Logic and Maths for Computing
In the example, how can we be sure that the propositions (1) through (3) given as
premises really do tautologically imply the end proposition (8)? The first answer
that comes to mind is that we are just applying the transitivity of `. But while ...
5
Logic, Thought and Action
But it is not tautologically implied by any tautology. For it is not tautological. Only
tautologies can strongly imply other tautologies. |=((Tautological Bp) ∧
Tautological (Ap ⇒ Bp)) ⇒ Tautological Ap Similarly |= □¬Ap ⇒ (Ap —∈ Bp).
Prove that every fonnula is tautologically equivalent to one that contains no
constants (l, T) and moreover, the only connectives in it are —\ and A. 18. Prove
that every formula is tautologically equivalent to one that does not contain the
constant ...
7
A Mathematical Introduction to Logic
If tautologically implies φ, then it follows that also logically implies φ. (See
Exercise 3.) But the converse fails. For example, ∀x Px logically implies Pc. But
∀x Px does not tautologically imply Pc, as ∀x Px and Pc are two different
sentence ...
Herbert Enderton, Herbert B. Enderton, 2001
8
Many-Valued Logics 1: Volume 1: Theoretical Foundations
Now, let XD be a set of truth-functional formulas of L, pairwise contradictory and
such that every formula, not tautologically equivalent to F, is tautologically
equivalent to a disjunction of formulas from XD. Assuming that X is a finite set of ...
Leonard Bolc, Piotr Borowik, 1992
9
A Course on Mathematical Logic
(b) Show that A I B I C andA I C I B are not tautologically equivalent. (c) Show that
A I B I C and (A I B) I C are not tautologically equivalent. ((1) Show that —\(A VB) \
/ C is a tautology if and only if both —\A \/C and —\B\/C are tautologies.
Shashi Mohan Srivastava, 2013
10
New Perspectives on Hegel's Philosophy of Religion
In its abstract universal character, the absolute is tautologically identical to itself
under the same universal description: being is being, force is force, the cosmic
substance is the cosmic substance, etc. It is, as Hegel says, "free equality with
itself ...
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tautologically w wiadomościach.
'Western' Diet Making The World Fatter, Less Healthy
70% of the world's population is expected to live in cities by 2050, and living in the city tautologically entails an urban lifestyle. It's pretty hard to grow vegetables ... «AskMen, Lip 15»
Rachmaninov's Symphony No 2 – which recording is best?
For the composer John Pickard this nod to Classical convention 'tautologically undermines the dramatic impact not only of the first movement but of the ... «Gramophone, Mar 15»
Why Robots Will Be The Biggest Job Creators In World History
... out with regularity, abundant job creation is always and everywhere the happy result of technological advances that tautologically lead to job destruction. «Lifeboat Foundation, Mar 15»
Tautological Description-Relativistic Metaphysics IS The Theory Of …
There is nothing more obvious than the tautology of that “I experience, therefore I experience”. Grounded on this tautologically self-evident start, Descartes' “I ... «Science 2.0, Lut 15»
Ask a Chef: How to Pick a Wine to Cook With
Typicity is basically a term for a tautologically tasting wine — like a very Chardonnay-y Chardonnay or a Merlot-y Merlot. Residual sugar is the term for any grape ... «Men's Journal, Lut 15»
Shallow Thoughts Run Deep
Deep thoughts stay tautologically close to reality. Put differently, deep thoughts run shallow. Example: “It is what it is.” In saying nothing, thoughts like this ... «PsychCentral.com, Lut 15»
Top VC: A lot of tech startup failure coming in 2015
“I think it's almost tautologically easier to execute a company that loses money than one that's profitable.” Sign up for Term Sheet, our daily newsletter on venture ... «Fortune, Sty 15»
WWE Body Slams Bootleggers in Appellate Ruling
"At best, Plaintiff defines Defendants almost tautologically: Defendants are anyone who would be a proper defendant within broad geographic and temporal ... «Hollywood Reporter, Lis 14»
A Response to “The Morons Pack Heat”
For the purpose of brevity, the bigotry and prejudice which saturate the early part of the article shall be treated as tautologically refuted. The author uses an ... «The Prince Arthur Herald, Wrz 14»
Iggy Azalea, Rita Ora break out katanas and jumpsuits for 'Black …
And what is up with Iggy's tautologically fraught line, “If it wasn't for you I wouldn't be stuck singing this song?” And has someone, possibly a close friend or family ... «Entertainment Weekly, Sie 14»
