Synergy User Manual and Tutorial. - THE CORE MEMORY
Synergy User Manual and Tutorial. - THE CORE MEMORY
Synergy User Manual and Tutorial. - THE CORE MEMORY
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<strong>Synergy</strong> <strong>User</strong> <strong>Manual</strong> <strong>and</strong> <strong>Tutorial</strong><br />
If we let Px be “x is a lawyer” <strong>and</strong> Qx be “x speaks the truth”, we have:<br />
∃x [Px ∧ Qx],<br />
which states that at least one lawyer speaks the truth. Quantifiers can be applied to more<br />
then one variable in a statement.<br />
Let P be “is a shoe in my closet”, where x is a right shoe <strong>and</strong> y is a left shoe. Then:<br />
∀x, ∃y[Px ∧ Py],<br />
is a symbolic representation of the statement: “For every right shoe in my closet, there<br />
exists a left shoe”. A mathematical statement would be:<br />
∃z ∈ N [x = y×z], x ∈ N, y ∈ N,<br />
which states that there exists an integer z, such that integer x is divisible by integer y. lx<br />
Modal Logic<br />
Modal logic extends the capabilities of traditional logic to include modal expressions,<br />
which contain premises such as “it is necessary that…” or “it is possible that…”. Modal<br />
logic is the study of deductive behavior of expressions based on necessary <strong>and</strong>/or<br />
possible premises. Modal logic can also be defined as a family of related logical systems<br />
that include logics for belief <strong>and</strong> temporal related expressions. The table below contains<br />
some common symbols <strong>and</strong> definitions used in the modal logic family:<br />
Logic Symbols Expressions Symbolized<br />
Modal Logic It is necessary that …<br />
◊<br />
It is possible that …<br />
Deontic Logic O It is obligatory that …<br />
P<br />
It is permitted that …<br />
F<br />
It is forbidden that …<br />
Temporal Logic<br />
G<br />
It will always be the case that …<br />
F<br />
It will be the case that …<br />
H<br />
It has always been the case that …<br />
P<br />
It was the case that…<br />
Doxastic Logic<br />
Bx<br />
x believes that …<br />
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