2021
DOI: 10.1007/978-3-030-71995-1_14
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Interpolation and Amalgamation for Arrays with MaxDiff

Abstract: In this paper, the theory of McCarthy’s extensional arrays enriched with a maxdiff operation (this operation returns the biggest index where two given arrays differ) is proposed. It is known from the literature that a diff operation is required for the theory of arrays in order to enjoy the Craig interpolation property at the quantifier-free level. However, the diff operation introduced in the literature is merely instrumental to this purpose and has only a purely formal meaning (it is obtained from the Skolem… Show more

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Cited by 5 publications
(17 citation statements)
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“…The third variant of the array theory we want to mention is the theory AX maxdi f f , where the axiom ( 8) is strengthened so that diff(a, b) returns the biggest index where a, b differ. This requires adding at least a symbol for a total ordering relation on the sort INDEX (we leave the reader to consult [20] for details). Under suitable mild hypotheses, it is possible to prove that the universal theory AX maxdi f f also has amalgamation and, hence, quantifier-free interpolation (but the proof is surprisingly much more delicate [20]).…”
Section: Strong Amalgamation and Combined Interpolationmentioning
confidence: 99%
See 3 more Smart Citations
“…The third variant of the array theory we want to mention is the theory AX maxdi f f , where the axiom ( 8) is strengthened so that diff(a, b) returns the biggest index where a, b differ. This requires adding at least a symbol for a total ordering relation on the sort INDEX (we leave the reader to consult [20] for details). Under suitable mild hypotheses, it is possible to prove that the universal theory AX maxdi f f also has amalgamation and, hence, quantifier-free interpolation (but the proof is surprisingly much more delicate [20]).…”
Section: Strong Amalgamation and Combined Interpolationmentioning
confidence: 99%
“…This requires adding at least a symbol for a total ordering relation on the sort INDEX (we leave the reader to consult [20] for details). Under suitable mild hypotheses, it is possible to prove that the universal theory AX maxdi f f also has amalgamation and, hence, quantifier-free interpolation (but the proof is surprisingly much more delicate [20]).…”
Section: Strong Amalgamation and Combined Interpolationmentioning
confidence: 99%
See 2 more Smart Citations
“…These are the main reasons why in [17] the theory has been further enriched. There, the semantics of diff, called maxdiff, is uniquely determined in the models of the theory and is more informative: it returns the biggest index where two different arrays differ.…”
Section: Introductionmentioning
confidence: 99%