Algorithmic correspondence and completeness in modal logic. V. Recursive extensions of SQEMA

The previously introduced algorithm SQEMA computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend SQEMA with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents of modal formulae in the extension of first-order logic with monadic least fixed-points FOμ. This computation operates by transforming input formulae into locally frame equivalent ones in the pure fragment of the hybrid μ-calculus. In particular, we prove that the recursive extension of SQEMA succeeds on the class of ‘recursive formulae’. We also show that a certain version of this algorithm guarantees the canonicity of the formulae on which it succeeds.     

Canonical word order and interference-based integration costs during sentence comprehension: The case of Spanish subject- and object-relative clauses

Object-relative clauses are generally harder to process than subject-relative clauses. Increased processing costs for object-relatives have been attributed either to working memory demands for the establishment of long-distance dependencies or to difficulties processing unexpected, noncanonical structures. The current study uses self-paced reading to contrast the impact of both kinds of factors in Spanish object-relative clauses, manipulating the interposition of the subject of the relative clause between object and verb. In addition, object-relatives were unambiguously marked at their onset with the Spanish preposition “a”. Reading times increased at the onset and final regions of object-relative clauses, regardless of interference-based working memory costs, although interference costs may affect the processing of post-relative-clause regions. These results suggest that, beyond interference-related working memory costs, end-of-clause integration processes may be affected by a preference for canonical structures, thus increasing processing difficulties when confronted with a noncanonical form.