We address the issue of providing sound and complete inference procedures for such languages.
Semi-lattices are associated with CI statements and a finite, sound and complete inference system relative to semi-lattice inclusions is presented.
The problem is that SOL, contrary to FOL, lacks a complete inference procedure: the price one pays for the greater expressive power of SOL is that there are no complete axiomatizations, as we have for FOL.
Recent versions of TrOWL are expected to produce complete inferences with our ontology while retaining the performance advantage of TrOWL over other reasoners (Yuan Ren, personal communication).
However, as male-mediated gene flow cannot be detected from mtDNA, more complete inferences of the phylogeographic history of a species should include biparentally or paternally inherited markers (e.g., [ 64, 65]), especially in species like the red fox where males disperse more than females [ 20].
Constraint set satisfiability is defined so that we can obtain a sound and complete type inference algorithm, by just transforming the relations defined in the type system into functions.
The facts that it is syntax-directed and type instantiation occurs only if required by a program context allow a sound and complete type inference algorithm to be obtained by transforming these relations into computable functions.
This work presents 1) a type system that permits to trace attributes and statically validate the composition against attributes lack or misuse and 2) a correct and complete type inference algorithm for this type system.
The language MLF is a proposal for a new type system that supersedes both ML and System F, allows for efficient, predictable, and complete type inference for partially annotated terms.
Michael Scriven (1959), for example, once objected to "the deductive model, with its syllogistic form, where no student of elementary logic could fail to complete the inference, given the premise", when no restriction is placed on the complexity of the relevant laws or the intricacy of these deductions (Hempel 1965c, 339).
Finally, properly modeling the correlation between two endpoints is necessary to complete proper inference (hypothesis tests, credible intervals, etc).
