In [1] Cameron and Hodges proved, by means of a combinatorial argument, that no compositional semantics for a logic of Imperfect Information such as Independence Friendly Logic [2] or Dependence Logic ([3]) may use sets of tuples of elements as meanings of formulas. However, Cameron and Hodges’ theorem fails if the domain of the semantics is restricted to infinite models only, and they conclude that Common sense suggests that there is no sensible semantics for CS on infinite structures A , using subsets of the domain of A as interpretations for formulas with one free variable. But we don’t know a sensible theorem along these lines ([1]). This work develops a formal, natural definition of “sensible semantics” according to which the statement quoted above can be proved.
Sensible Semantics of Imperfect Information
Galliani P
2011-01-01
Abstract
In [1] Cameron and Hodges proved, by means of a combinatorial argument, that no compositional semantics for a logic of Imperfect Information such as Independence Friendly Logic [2] or Dependence Logic ([3]) may use sets of tuples of elements as meanings of formulas. However, Cameron and Hodges’ theorem fails if the domain of the semantics is restricted to infinite models only, and they conclude that Common sense suggests that there is no sensible semantics for CS on infinite structures A , using subsets of the domain of A as interpretations for formulas with one free variable. But we don’t know a sensible theorem along these lines ([1]). This work develops a formal, natural definition of “sensible semantics” according to which the statement quoted above can be proved.
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