Time-Stamped Claim Logic

The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e., as a logic per se, but also because it has a number of practical applications, in particular when one needs to reason about a huge amount of pieces of evidence collected from different sources, where some of the pieces of evidence may be contradictory and some sources are considered to be more trustworthy than others. We introduce the Time-Stamped Claim Logic including a sound and complete sequent calculus that allows one to reduce the size of the collected set of evidence and removes inconsistencies, i.e., the logic ensures that the result is consistent with respect to the trust relations considered. In order to show how Time-Stamped Claim Logic can be used in practice, we consider a concrete cyber-attribution case study.

[1]  Benjamin Aziz,et al.  Modelling and refinement of forensic data acquisition specifications , 2014, Digit. Investig..

[2]  Phan Minh Dung,et al.  On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games , 1995, Artif. Intell..

[3]  Nicole Beebe,et al.  Digital Forensic Research: The Good, the Bad and the Unaddressed , 2009, IFIP Int. Conf. Digital Forensics.

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

[5]  Thomas Studer,et al.  Justifications for common knowledge , 2010, J. Appl. Non Class. Logics.

[6]  Rajesh Kumar Goutam,et al.  The Problem of Attribution in Cyber Security , 2015 .

[7]  Walter Carnielli,et al.  An epistemic approach to paraconsistency: a logic of evidence and truth , 2019, Synthese.

[8]  W. Hoek,et al.  Dynamic Epistemic Logic , 2007 .

[9]  Constantin A. Drossos Probability and Logic , 2004 .

[10]  Mohammed H. Almeshekah,et al.  Planning and Integrating Deception into Computer Security Defenses , 2014, NSPW '14.

[11]  Cristina Sernadas,et al.  Preservation of Craig interpolation by the product of matrix logics , 2013, J. Appl. Log..

[12]  S. Artemov Explicit Provability and Constructive Semantics , 2001, Bulletin of Symbolic Logic.

[13]  Sergei N. Artëmov THE LOGIC OF JUSTIFICATION , 2008, The Review of Symbolic Logic.

[14]  Melvin Fitting A quantified logic of evidence , 2008, Ann. Pure Appl. Log..

[15]  Mohammed H. Almeshekah,et al.  Cyber Security Deception , 2016, Cyber Deception.

[16]  Xindong Wu,et al.  On digital image trustworthiness , 2016, Appl. Soft Comput..

[17]  Johan van Benthem,et al.  Logical Dynamics of Evidence , 2011, LORI.

[18]  Zoran Ognjanovic,et al.  Probabilistic Justification Logic , 2016, LFCS.

[19]  Emil C. Lupu,et al.  An Argumentation-Based Approach to Assist in the Investigation and Attribution of Cyber-Attacks , 2019, ArXiv.

[20]  Gregory N. Larsen,et al.  Techniques for Cyber Attack Attribution , 2003 .

[21]  Joseph Y. Halpern,et al.  A Logic for Reasoning about Evidence , 2002, UAI.

[22]  Emil C. Lupu,et al.  Helping Forensic Analysts to Attribute Cyber-Attacks: An Argumentation-Based Reasoner , 2018, PRIMA.

[23]  Cristina Sernadas,et al.  A Roadmap to Decidability , 2015 .

[24]  Alexandru Baltag,et al.  The logic of justified belief, explicit knowledge, and conclusive evidence , 2014, Ann. Pure Appl. Log..

[25]  Joseph Lurie,et al.  Probabilistic Justification Logic , 2018 .

[26]  Dov M. Gabbay,et al.  A Logical Account of Formal Argumentation , 2009, Stud Logica.

[27]  Luca Viganò,et al.  A Formal Approach to Analyzing Cyber-Forensics Evidence , 2018, ESORICS.

[28]  Luca Viganò,et al.  Fibring Labelled Deduction Systems , 2002, J. Log. Comput..

[29]  Mauro Barni,et al.  A Framework for Decision Fusion in Image Forensics Based on Dempster–Shafer Theory of Evidence , 2013, IEEE Transactions on Information Forensics and Security.

[30]  Johan van Benthem,et al.  Evidence Logic: A New Look at Neighborhood Structures , 2012, Advances in Modal Logic.

[31]  Dov M. Gabbay,et al.  Fibring Argumentation Frames , 2009, Stud Logica.