@article {3094113, title = {A contextual type theory with judgemental modalities for reasoning from open assumptions}, journal = {Logique et Analyse}, volume = {55}, number = {220}, year = {2012}, pages = {579{\textendash}600}, abstract = {

Contextual type theories are largely explored in their applications to programming languages, but less investigated for knowledge representation purposes. The combination of a constructive language with a modal extension of contexts appears crucial to explore the attractive idea of a type-theoretical calculus of provability from refutable assumptions for non-monotonic reasoning. This paper introduces such a language: the modal operators are meant to internalize two different modes of correctness, respectively with necessity as the standard notion of constructive verification and possibility as provability up to refutation of contextual conditions.

}, issn = {0024-5836}, author = {Primiero, Giuseppe} } @conference {1166760, title = {Constructive contextual modal judgments for reasoning from open assumptions}, booktitle = {Proceedings of the Computability in Europe 2010 Conference}, year = {2010}, publisher = {Centre for Applied Mathematics and Information Technology, Department of Mathematics, University of Azores}, organization = {Centre for Applied Mathematics and Information Technology, Department of Mathematics, University of Azores}, abstract = {

Dependent type theories using a structural notion of context are largely explored in their applications to programming languages, but less investigated for knowledge representation purposes. In particular, types with modalities are already used for distributed and staged computation. This paper introduces a type system extended with judgmental modalities internalizing epistemically different modes of correctness to explore a calculus of provability from refutable assumptions.

}, author = {Primiero, Giuseppe}, editor = {Ferreira, F and Guerra, H and Mayordomo, E and Rasga, J} } @conference {810575, title = {A constructive modal semantics for contextual verification}, booktitle = {Proceedings of the First International Workshop on Logic-Based Interpretation of Context: Modeling and Applications}, year = {2009}, publisher = {CEUR-Workshop Proceedings}, organization = {CEUR-Workshop Proceedings}, abstract = {

This paper introduces a non-standard semantics for a modal version of constructive KT for contextual (assumptions-based) verification. The modal fragment expresses verifiability under extensions of contexts, enjoying adapted validity and (weak) monotonicity properties depending on satisfaction of the contextual data.

}, url = {http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-550/}, author = {Primiero, Giuseppe} }