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56 views

Where can I learn more about these two functions obtained from IFF and XOR?

Given a set $X$, write $\mathrm{heaps}(X)$ for the set of all finite heaps (or 'multisets', if you prefer) on $X$. Under this definition, it is well-known that if a binary operation $*$ on a set $X$ ...
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93 views

Gap in Halmos & Givant's “Logic as Algebra”: undefined $\models$?

I have been hugely enjoying Logic as Algebra by Halmos and Givant (1998, isbn: 0-88385-327-2)1, largely because I appreciate the authors' careful attention to the ...
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137 views

meaning of ``partial converse''

In the definition of a commutative ring $(R,+,\times)$, one of the postulates given is that of uniqueness, i.e. that $$ a=a', b=b'\implies a+b=a'+b', ab=a' b'.$$ The text states that for the system ...
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111 views

Generalized “Duality” of Classical Propositional Logical Operations

Duality in propositional logic between conjunction and disjunction, $K$ and $A$ means that for any "identity", such as $KpNp = 0$ (ignoring the detail of how to define this notion in propositional ...