Interpolation in extensions of first-order logic (Q2186699)

The paper targets knowledge bases with ``singular geometric rules'', essentially disjunctive rules with existential variables. The interpolation theorem is extended to classic and intuitionistic sequent calculi with geometric rules, and several extensions of first-order logic are obtained as special cases of such calculi. In particular, the authors show how to obtain first-order logic with identity, the theory of equivalence relations, (strict) partial and linear orders, the theory of apartness and the theory of positive partial and linear orders. A nice reading presenting several interesting results.