Thinking About Causation: A Causal Language with Epistemic Operators

This paper proposes a formal framework for modeling the interaction of causal and (qualitative) epistemic reasoning. To this purpose, we extend the notion of a causal model with a representation of the epistemic state of an agent. On the side of the object language, we add operators to express knowledge and the act of observing new information. We provide a sound and complete axiomatization of the logic, and discuss the relation of this framework to causal team semantics.

[1]  Lawrence S. Moss,et al.  The Logic of Public Announcements and Common Knowledge and Private Suspicions , 1998, TARK.

[2]  Johan van Benthem,et al.  Logical Dynamics of Information and Interaction , 2014 .

[3]  Joseph Y. Halpern,et al.  Responsibility and Blame: A Structural-Model Approach , 2003, IJCAI.

[4]  Fan Yang,et al.  Counterfactuals and Dependencies on Causal Teams: Expressive Power and Deduction Systems , 2020, AiML.

[5]  Joseph Y. Halpern Axiomatizing Causal Reasoning , 1998, UAI.

[6]  R. H. Strotz,et al.  RECURSIVE VS. NONRECURSIVE SYSTEMS: AN ATTEMPT AT SYNTHESIS (PART I OF A TRIPTYCH ON CAUSAL CHAIN SYSTEMS) , 1960 .

[7]  Yanjing Wang,et al.  Knowing Values and Public Inspection , 2016, ICLA.

[8]  Alexandru Baltag,et al.  Causal Agency and Responsibility: A Refinement of STIT Logic , 2020 .

[9]  Wilfrid Hodges,et al.  Compositional Semantics for a Language of Imperfect Information , 1997, Log. J. IGPL.

[10]  Joseph Y. Halpern,et al.  Actual Causality , 2016, A Logical Theory of Causality.

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

[12]  Paul Evans,et al.  A Tale of Two Effects , 2008, The Review of Economics and Statistics.

[13]  Jouko Vnnen,et al.  Dependence Logic: A New Approach to Independence Friendly Logic (London Mathematical Society Student Texts) , 2007 .

[14]  Yanjing Wang,et al.  On axiomatizations of public announcement logic , 2013, Synthese.

[15]  J. Pearl Causal diagrams for empirical research , 1995 .

[16]  J. Pearl Causality: Models, Reasoning and Inference , 2000 .

[17]  Tom Burr,et al.  Causation, Prediction, and Search , 2003, Technometrics.

[18]  Mélanie Frappier,et al.  The Book of Why: The New Science of Cause and Effect , 2018, Science.

[19]  Jelle Gerbrandy,et al.  Dynamic epistemic logic , 1998 .

[20]  Thomas Icard,et al.  Probabilistic Reasoning across the Causal Hierarchy , 2020, AAAI.

[21]  Gabriel Sandu,et al.  Interventionist Counterfactuals on Causal Teams , 2019, CREST@ETAPS.

[22]  Alexandru Baltag,et al.  To Know is to Know the Value of a Variable , 2016, Advances in Modal Logic.

[23]  Rachael Briggs,et al.  Interventionist counterfactuals , 2012 .

[24]  Merlijn Sevenster,et al.  Independence-Friendly Logic - a Game-Theoretic Approach , 2011, London Mathematical Society lecture note series.

[25]  Jouko A. Väänänen,et al.  Dependence Logic - A New Approach to Independence Friendly Logic , 2007, London Mathematical Society student texts.