A Proof Theoretic Interpretation of Model Theoretic Hiding
Logical frameworks like LF are used for formal representations of logics in order to make them amenable to formal machine-assisted meta-reasoning. While the focus has originally been on logics with a proof theoretic semantics, we have recently shown how to define model theoretic logics in LF as well. We have used this to define new institutions in the Heterogeneous Tool Set in a purely declarative way.
It is desirable to extend this model theoretic representation of logics to the level of structured specifications. Here a particular challenge among structured specification building operations is hiding, which restricts a specification to some export interface. Specification languages like ASL and CASL support hiding, using an institution-independent model theoretic semantics abstracting from the details of the underlying logical system.
Logical frameworks like LF have also been equipped with structuring languages. However, their proof theoretic nature leads them to a theory-level semantics without support for hiding. In the present work, we show how to resolve this difficulty.
KeywordsType Family Logical Framework Signature Graph Signature Morphism Proof Theoretic Semantic
Unable to display preview. Download preview PDF.
- [Bar92]Barendregt, H.: Lambda calculi with types. In: Abramsky, S., Gabbay, D., Maibaum, T. (eds.) Handbook of Logic in Computer Science, vol. 2, Oxford University Press (1992)Google Scholar
- [CHK+10]Codescu, M., Horozal, F., Kohlhase, M., Mossakowski, T., Rabe, F., Sojakova, K.: Towards Logical Frameworks in the Heterogeneous Tool Set Hets. In: Workshop on Abstract Development Techniques (2010)Google Scholar
- [HR11]Horozal, F., Rabe, F.: Representing Model Theory in a Type-Theoretical Logical Framework. Theoretical Computer Science (to appear, 2011), http://kwarc.info/frabe/Research/HR_folsound_10.pdf
- [IR11]Iancu, M., Rabe, F.: Formalizing Foundations of Mathematics. Mathematical Structures in Computer Science (to appear, 2011), http://kwarc.info/frabe/Research/IR_foundations_10.pdf
- [KMR09]Kohlhase, M., Mossakowski, T., Rabe, F.: The LATIN Project (2009), https://trac.omdoc.org/LATIN/
- [ML74]Martin-Löf, P.: An Intuitionistic Theory of Types: Predicative Part. In: Proceedings of the 1973 Logic Colloquium, pp. 73–118. North-Holland (1974)Google Scholar
- [Rab10]Rabe, F.: A Logical Framework Combining Model and Proof Theory. Submitted to Mathematical Structures in Computer Science (2010), http://kwarc.info/frabe/Research/rabe_combining_09.pdf
- [RK10]Rabe, F., Kohlhase, M.: A Scalable Module System (2010), http://kwarc.info/frabe/Research/mmt.pdf
- [RS09]Rabe, F., Schürmann, C.: A Practical Module System for LF. In: Cheney, J., Felty, A. (eds.) Proceedings of the Workshop on Logical Frameworks: Meta-Theory and Practice (LFMTP), pp. 40–48. ACM Press (2009)Google Scholar
- [SW83]Sannella, D., Wirsing, M.: A kernel language for algebraic specification and implementation. In: ADT (1983)Google Scholar
- [ZK09]Zholudev, V., Kohlhase, M.: TNTBase: a Versioned Storage for XML. In: Proceedings of Balisage: The Markup Conference 2009. Balisage Series on Markup Technologies, vol. 3. Mulberry Technologies, Inc. (2009)Google Scholar