We investigate the effect on the complexity of adding the universal modality and the reflexive transitive closure modality to modal logics. From the examples in the literature, one might conjecture that adding the reflexive transitive closure modality is at least as hard as adding the universal modality, and that adding either of these modalities to a multi-modal logic where the modalities do not interact can only increase the complexity to EXPTIME-complete. We show that the first conjecture holds under reasonable assumptions (...) and that, except for a number of special cases which we fully characterize, the hardness part of the second conjecture is true. However, the upper bound part of the second conjecture fails miserably: we show that there exists a uni-modal, decidable, finitely axiomatizable, and canonical logic for which adding the universal modality causes undecidability and for which adding the reflexive transitive closure modality causes high undecidability. (shrink)

Until recently, cognitive science focused on such mental functions as problem solving, grammar, and pattern-the functions in which the human mind most closely resembles a computer. But humans are more than computers: we invent new meanings, imagine wildly, and even have ideas that have never existed before. Today the cutting edge of cognitive science addresses precisely these mysterious, creative aspects of the mind.The Way We Think is a landmark analysis of the imaginative nature of the mind. Conceptual blending is already (...) widely known in research laboratories throughout the world; this book, written to be accessible to both lay readers and interested scientists, is its definitive statement. Gilles Fauconnier and Mark Turner show that conceptual blending is the root of the cognitively modern human mind, and that conceptual blends themselves are continually combined and reblended to create the rich mental fabric in which we live.The Way We Think shows how this blending operates; how it is affected by (and gives rise to) language, identity, culture, and invention; and how we imagine what could be and what might have been. The result is a bold and exciting new view of how the mind works. (shrink)