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That is, classical and intuitionistic implications collapse in the combined logic.
It is worth noting that the previous arguments depart from a very strong assumption: that the metaproperty DMT is preserved in the combined logic.
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The combined logic should be minimal in some sense: that is, if L is obtained from L1 and L2 by some combination process, it should be expected that: 1) L extends both L1 and L2; and 2) L is a minimal extension of both L1 and L2.
Besides the definition of the appropriate language for the combined logic, another important question that immediately arises is: should the logics L1 and L2 (to be combined) be presented in the same way?
As a consequence, the combined logic of negation and disjunction (which can be defined as the logic over ¬ and ∨ characterized by the valuations over {0,1} satisfying both clauses above) validates, and so classical logic is recovered.
No additional mixing principles are mandatory for the combined logic of many agents, but bridge axioms may of course be added.
For instance, the definition of the language of parameterization is fundamental in order to obtain the intended combined logic (see Subsection 4.5).
In fact, it contradicts a basic criterion of fibring (and also of fusion), as expressed in Gabbay 1999: given logic systems L1 and L2, the combination of L1 and L2 should be the smallest logic system in the combined language which is a conservative extension of both L1 and L2.
The recommendations presented here are based on a combined logic and implementation analysis.
An immediate 2percentt increase in the combined payroll taxes.
In the combined cash of the national party committees, Republicans had $55.5 million; Democrats $87.1 million.
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