Dynamic Causal Calculus

We introduce dynamic causal calculus, a nonmonotonic formalism that can be viewed as a direct logical counterpart of the action description language C+ from (Giunchiglia et al. 2004). We formulate a nonmonotonic semantics of the associated causal language, and compare this semantics with the indirect, two-stage semantics for C+, given in (Giunchiglia et al. 2004). It will be shown, in particular, that the suggested semantics allows us to alleviate syntactic distinctions between propositional atoms, maintained by C+, as well as type restrictions imposed on its causal laws. We will describe also a logical formalism of dynamic causal inference that constitutes a complete description of the logic that is adequate for this dynamic calculus.

[1]  Hector Geffner,et al.  Causal Theories for Nonmonotonic Reasoning , 1990, AAAI.

[2]  Michael Gelfond,et al.  Action Languages , 1998, Electron. Trans. Artif. Intell..

[3]  Murray Shanahan.  Solving the frame problem - a mathematical investigation of the common sense law of inertia , 1997 .

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

[5]  Jerzy Tiuryn,et al.  Dynamic logic , 2001, SIGA.

[6]  Alexander Bochman,et al.  A causal approach to nonmonotonic reasoning , 2004, Artif. Intell..

[7]  Joohyung Lee,et al.  Action Language BC+: Preliminary Report , 2015, AAAI.

[8]  Allen P. Hazen,et al.  On the Ternary Relation and Conditionality , 2012, J. Philos. Log..

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

[10]  Yde Venema,et al.  Dynamic Logic by David Harel, Dexter Kozen and Jerzy Tiuryn. The MIT Press, Cambridge, Massachusetts. Hardback: ISBN 0–262–08289–6, $50, xv + 459 pages , 2002, Theory and Practice of Logic Programming.

[11]  Alexander Bochman,et al.  A Causal Theory of Abduction , 2007, J. Log. Comput..

[12]  Raymond Reiter,et al.  The Frame Problem in the Situation Calculus: A Simple Solution (Sometimes) and a Completeness Result for Goal Regression , 1991, Artificial and Mathematical Theory of Computation.

[13]  Giuseppe De Giacomo,et al.  Linear Temporal Logic and Linear Dynamic Logic on Finite Traces , 2013, IJCAI.

[14]  Enrico Giunchiglia,et al.  Dependent Fluents , 1995, IJCAI.

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

[16]  Y. Venema.  A crash course in arrow logic , 1994 .

[17]  Raymond Reiter,et al.  Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems , 2001 .

[18]  Alexander Bochman,et al.  Logic in Nonmonotonic Reasoning , 2011 .

[19]  M. Shanahan.  Solving the frame problem , 1997 .

[20]  Johan van Benthem,et al.  A note on dynamic arrow logic , 1994 .

[21]  Enrico Giunchiglia,et al.  Nonmonotonic causal theories , 2004, Artif. Intell..

[22]  Illtyd Trethowan.  Causality , 1938 .

[23]  Enrico Giunchiglia,et al.  An Action Language Based on Causal Explanation: Preliminary Report , 1998, AAAI/IAAI.

[24]  David E. Smith,et al.  The Persistence of Derived Information , 1988, AAAI.

[25]  Diego Calvanese,et al.  Reasoning about Actions and Planning in LTL Action Theories , 2002, KR.

[26]  Hudson Turner,et al.  A Logic of Universal Causation , 1999, Artif. Intell..

[27]  Fangzhen Lin,et al.  Embracing Causality in Specifying the Indirect Effects of Actions , 1995, IJCAI.

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