Modeling of Phenomena and Dynamic Logic of Phenomena

Modeling of complex phenomena such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, problem or theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models.

[1]  F. Delizy Visual Data Mining Using Monotone Boolean Functions , 2003 .

[2]  Robert W. Binkley The Logic of Action , 1976 .

[3]  Hartry Field Mental representation , 2021, Encyclopedia of Autism Spectrum Disorders.

[4]  Boris Kovalerchuk,et al.  Data mining in finance: advances in relational and hybrid methods , 2000 .

[5]  Gregory Wheeler AGM Belief Revision in Monotone Modal Logics , 2010 .

[6]  Lawrence S. Moss,et al.  Logics for Epistemic Programs , 2004, Synthese.

[7]  Leon van der Torre,et al.  Constraints for Input/Output Logics , 2001, J. Philos. Log..

[8]  Boris Kovalerchuk,et al.  Data mining in finance , 2000 .

[9]  Johan van Benthem,et al.  Exploring logical dynamics , 1996, Studies in logic, language and information.

[10]  L. Perlovsky Toward physics of the mind: Concepts, emotions, consciousness, and symbols , 2006 .

[11]  Leendert van der Torre,et al.  Normative framework for normative system change , 2009, AAMAS.

[12]  Vaughan R. Pratt A practical decision method for propositional dynamic logic (Preliminary Report) , 1978, STOC '78.

[13]  Henry E. Kyburg,et al.  The Logic of Risky Knowledge , 2002, WoLLIC.

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

[15]  Leon van der Torre,et al.  Input/Output Logics , 2000, J. Philos. Log..

[16]  David Poole,et al.  A Logical Framework for Default Reasoning , 1988, Artif. Intell..

[17]  M. de Rijke,et al.  Modal Logic , 2001, Cambridge Tracts in Theoretical Computer Science.

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

[19]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[20]  Hannes Leitgeb,et al.  Dynamic doxastic logic: why, how, and where to? , 2007, Synthese.

[21]  Henry E. Kyburg,et al.  Conditionals and consequences , 2007, J. Appl. Log..

[22]  Jeffrey C. King Context Dependent Quantifiers and Donkey Anaphora , 2004 .

[23]  Horacio L. Arló-Costa First Order Extensions of Classical Systems of Modal Logic; The role of the Barcan schemas , 2002, Stud Logica.

[24]  Johan van Benthem,et al.  Dynamic logic for belief revision , 2007, J. Appl. Non Class. Logics.

[25]  Leonid Perlovsky,et al.  Neural Networks and Intellect: Using Model-Based Concepts , 2000, IEEE Transactions on Neural Networks.

[26]  Jonathan Barzilai,et al.  On the foundations of measurement , 2001, 2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat.No.01CH37236).

[27]  Evangelos Triantaphyllou,et al.  Interactive Learning of Monotone Boolean Functions , 1996, Inf. Sci..

[28]  P. Spirtes,et al.  Causation, Prediction, and Search, 2nd Edition , 2001 .

[29]  L.i. Perlovsky,et al.  Evolution of Languages, Consciousness and Cultures , 2007, IEEE Computational Intelligence Magazine.

[30]  Choh Man Teng,et al.  Robustness of Evidential Probability , 2010 .

[31]  Bernhard Beckert,et al.  Dynamic Logic , 2007, The KeY Approach.

[32]  T. Gelder,et al.  What Might Cognition Be, If Not Computation? , 1995 .

[33]  Marco Alberti,et al.  NO Revision and NO Contraction , 2011, Minds and Machines.

[34]  Alexandru Baltag,et al.  A Dynamic-Logical Perspective on Quantum Behavior , 2008, Stud Logica.

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