论文信息 - Logics for multi-subset spaces

Logics for multi-subset spaces

We generalize Moss and Parikh's logic of knowledge, effort, and topological reasoning, in two ways. We develop both a multi-agent and a multi-method setting for it. In each of these cases, we prove a corresponding soundness and completeness theorem, and we show that the new logics are decidable. Our methods of proof rely on those for the original system. This might have been expected, since that system is conservatively extended for the given situation. Several technical details are different nevertheless here.

Bernhard Heinemann | B. Heinemann

[1] W. van der Hoek,et al. Epistemic logic for AI and computer science , 1995, Cambridge tracts in theoretical computer science.

[2] Johan van Benthem,et al. Handbook of Spatial Logics , 2007 .

[3] Lawrence S. Moss,et al. Topological Reasoning and the Logic of Knowledge , 1996, Ann. Pure Appl. Log..

[4] Johan van Benthem,et al. Reasoning About Space: The Modal Way , 2003, J. Log. Comput..

[5] Mark Ryan,et al. Ideal Agents Sharing (some!) Knowledge , 1998, ECAI.

[6] Ronald Fagin,et al. Reasoning about knowledge , 1995 .

[7] Bernhard Heinemann,et al. Topology and Knowledge of Multiple Agents , 2008, IBERAMIA.

[8] A. Tarski,et al. The Algebra of Topology , 1944 .

[9] Rohit Parikh,et al. Completeness of Certain Bimodal Logics for Subset Spaces , 2002, Stud Logica.

[10] R. Goldblatt. Logics of Time and Computation , 1987 .

[11] Konstantinos Georgatos,et al. Modal Logics for Topological Spaces , 2000, ArXiv.

[12] Konstantinos Georgatos,et al. Knowledge Theoretic Properties of Topological Spaces , 1992, Logic at Work.

[13] Richard Spencer-Smith,et al. Modal Logic , 2007 .

[14] Bernhard Heinemann. A Two sorted Hybrid Logic Including Guarded Jumps , 2004, Advances in Modal Logic.