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1
Encyclopaedia of Mathematics, Supplement III
It turns out that there is a close connection between the deduction theorem and
the universal algebraic notion of definable principal congruence relations. The
development of abstract algebraic logic was motivated in part by a desire to
provide ...
2
Handbook of Philosophical Logic
In case (1), a+ = — □• — — > (-1*7+ — > (»7+ — > <5+)), which is not an
instance of an axiom in mCi*. However, it is immediate to see that a+ is a theorem
of mCi , because of axioms (bcl)', (ci)' and by the deduction theorem. Indeed, #7+
...
Dov M. Gabbay, Franz Guenthner,
2007
3
Automated
Deduction - Cade-13: 13th International Conference ...
The Deduction Theorem We cannot prove openended versions of all
metatheorems. An example of a metatheorem which does not hold in all theory
extensions is the deduction theorem, which is one of the more important
metatheorems about ...
Michael A. McRobbie, J.K. Slaney,
1996
4
Formal Modeling: Actors; Open Systems, Biological Systems: ...
6 The Deduction Theorem Revisited 6.1 Formalizing the Deduction Theorem The
parameterized versions of the deduction theorem can now be expressed as
metatheoretic statements relating the initial models of all the different
instantiations ...
Gul Agha, Olivier Danvy, José Meseguer,
2011
5
Foundations of Logic and Mathematics: Applications to ...
Still with the hypothesis N, after the completion of any operation (D1)-(D3) on
step P, the Deduction Theorem then performs the same operations (D1)-(D3) on
each of the following steps, Q,...,R. After the completion of operations (D1)-(D3)
on ...
6
Advances in Logic, Artificial Intelligence, and Robotics: ...
[3J— 2 A conjunctive deduction theorem. We have shown the following theorem
from Herhrand's Deduction Theorem.[ ] Theorem 1. lf K"p,+, \- r, then K"~'p, \- Cp.,
+ ir. We use often this theorem. Applying the deduction theorem to Theorem ...
Jair Minoro Abe, João Inácio da Silva Filho,
2002
7
FST TCS 2000: Foundations of Software Technology and ...
Our example is a standard one in metareasoning, namely, the deduction theorem
. 8.1 The Deduction Theorem for Minimal Logic We present here the deduction
theorem for minimal logic of implication. This theorem is interesting for several ...
Sanjiv Kapoor, Sanjiva Prasad,
2000
\~T A means that A is provable in the object- theory T, and T[B] is the theory T
extended with the axiom B, then the deduction theorem says If r-T[B] A, then hr B
=> A. This is an interesting theorem for several reasons. First, it is an explicitly ...
Gérard Huet, Gordon Plotkin,
1993
9
First Order Mathematical Logic
Prove ~ P i- P -> 14 The Deduction Theorem We write "A, P i-Q" for "A U {P} i-Q."
The deduction theorem is If A, Pi-Q, then A i-P->Q Before proving the theorem, we
give some examples. EXAMPLE 1. Theorem 13.2 is ~A(x) i- A(x) ->B(y).
10
Logic, Induction and Sets
4.1.1.1 The deduction theorem The deduction theorem for a logic L is the
assertion if L,A\- B, then L h A ^ B. The converse is easy. THEOREM 19 The
deduction theorem holds for L iff L contains (all substitution instances of) K and S.
Proof: The ...