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This book is an example of fruitful interaction between (non-classical) propo sitionallogics and (classical) model theory which was made possible due to categorical logic. Its main aim consists in investigating the existence of model completions for equational theories arising from propositional logics (such as the theory of Heyting algebras and various kinds of theories related to proposi tional modal logic ). The existence of model-completions turns out to be related to proof-theoretic facts concerning interpretability of second order propositional logic into ordinary propositional logic...

This book is an example of fruitful interaction between (non-classical) propo sitionallogics and (classical) model theory which was made possible due to categorical logic. Its main aim consists in investigating the existence of model completions for equational theories arising from propositional logics (such as the theory of Heyting algebras and various kinds of theories related to proposi tional modal logic ). The existence of model-completions turns out to be related to proof-theoretic facts concerning interpretability of second order propositional logic into ordinary propositional logic...

This volume contains the proceedings of the 7th International Symposium of Frontiers of Combining Systems (FroCoS 2009) held during September 16-18, 2009 in Trento, Italy. Previous FroCoS meetings were organized in Munich (1996), Amsterdam (1998), Nancy (2000), Santa Margherita Ligure (2002), - enna (2005), and Liverpool (2007). In 2004, 2006, and 2008 FroCoS joined IJCAR, the International Joint Conference on Automated Reasoning. Like its predecessors, FroCoS 2009 o?ered a forum for the presentation and discussion of research activities on the combination, integration, analysis, m-...

Modal logic is a subject with ancient roots in the western logical tradition. Up until the last few generations, it was pursued mainly as a branch of philosophy. But in recent years, the subject has taken new directions with connections to topics in computer science and mathematics. This volume is the proceedings of the conference of record in its fi eld, Advances in Modal Logic. Its contributions are state-of-the-art papers. The topics include decidability and complexity results for specifi c modal logics, proof theory of modal logic, logics for reasoning about time and space, provability...