ON FORMALIZING CAUSATION BASED ON CONSTANT CONJUNCTION THEORY

Abstract Constant conjunction theory of causation had been the dominant theory in philosophy for a long time and regained attention recently. This paper gives a logical framework of causation based on the theory. The basic idea is that causal statements are empirical, and are derived from our past experience by observing constant conjunction between objects. The logic is defined on linear time structures. A causal statement is evaluated at time points, such that its value depends on what has been in the past. We first give a semantics that contains basic conditions that, we think, must hold for a concept of causation, on which we define the minimal causal logic. Then we discuss its possible extensions for various concepts of causation. Complete deductive systems are given.

[1]  Mark Reynolds,et al.  Temporal logic , 2007, Handbook of Modal Logic.

[2]  D. Gabbay,et al.  Temporal Logic Mathematical Foundations and Computational Aspects , 1994 .

[3]  Michael Baumgartner,et al.  Regularity Theories Reassessed , 2008 .

[4]  J. Knott.  The organization of behavior: A neuropsychological theory , 1951 .

[5]  Laura Giordano,et al.  Ramification and causality in a modal action logic , 2000, J. Log. Comput..

[6]  Fangzhen Lin,et al.  Embracing Causality in Specifying the Indeterminate Effects of Actions , 1996, AAAI/IAAI, Vol. 1.

[7]  J. Mackie,et al.  I . CAUSES AND CONDITIONS , 2008 .

[8]  Camilla Schwind,et al.  Causality in Action Theories , 1999, Electron. Trans. Artif. Intell..

[9]  Richard S. Sutton,et al.  Reinforcement Learning: An Introduction , 1998, IEEE Trans. Neural Networks.

[10]  J. Mackie,et al.  The cement of the universe : a study of causation , 1977 .

[11]  Michael Thielscher,et al.  Ramification and Causality , 1997, Artif. Intell..

[12]  Norman Y. Foo,et al.  EPDL: A Logic for Causal Reasoning , 2001, IJCAI.

[13]  Helen Beebee,et al.  Does Anything Hold the Universe Together? , 2006, Synthese.

[14]  Ned Hall.  Two Concepts of Causation , 2001 .

[15]  Illtyd Trethowan.  Causality , 1938 .

[16]  Joseph Y. Halpern,et al.  Causes and Explanations: A Structural-Model Approach. Part I: Causes , 2000, The British Journal for the Philosophy of Science.

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

[18]  Ned Hall,et al.  Causation and counterfactuals , 2004 .

[19]  Franz von Kutschera,et al.  Causation , 1993, J. Philos. Log..

[20]  Ned Hall.  Causation and the Price of Transitivity , 2000 .

[21]  Donald Nute,et al.  Counterfactuals , 1975, Notre Dame J. Formal Log..

[22]  Dov M. Gabbay,et al.  Handbook of Philosophical Logic , 2002 .

[23]  Max Black,et al.  Why Cannot an Effect Precede its Cause , 1956 .

[24]  Keith A. Markus,et al.  Making Things Happen: A Theory of Causal Explanation , 2007 .

[25]  Frank Wolter,et al.  Handbook of Modal Logic , 2007, Studies in logic and practical reasoning.

[26]  Tom L. Beauchamp,et al.  An enquiry concerning human understanding : a critical edition , 2000 .

[27]  Michael Baumgartner,et al.  Uncovering deterministic causal structures: a Boolean approach , 2009, Synthese.

[28]  Nuel D. Belnap,et al.  Seeing To it That: A Canonical Form for Agentives , 2008 .

[29]  D. Lewis.  Causation as Influence , 2000 .

[30]  T. Troward.  Causes and conditions. , 1919 .

[31]  A. E. Dummett,et al.  Symposium: “Can An Effect Precede Its Cause?” , 1954 .

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

[33]  Ming Xu,et al.  Causation in Branching Time (I): Transitions, Events and Causes , 1997, Synthese.

[34]  Hudson Turner,et al.  Causal Theories of Action and Change , 1997, AAAI/IAAI.

[35]  W. Bean.  Patterns of Discovery : An Inquiry into the Conceptual Foundations of Science. , 1960 .

[36]  Michael Esfeld,et al.  Current Issues in Causation , 2001 .

[37]  Yde Venema,et al.  Derivation rules as anti-axioms in modal logic , 1993, Journal of Symbolic Logic.

[38]  Laura Giordano,et al.  Conditional logic of actions and causation , 2004, Artif. Intell..