# Dynamic epistemic logic of belief change in legal judgments

## Abstract

This study realizes belief/reliability change of a judge in a legal judgment by dynamic epistemic logic (DEL). A key feature of DEL is that possibilities in an agent’s belief can be represented by a Kripke model. This study addresses two difficulties in applying DEL to a legal case. First, since there are several methods for constructing a Kripke model, our question is how we can construct the model from a legal case. Second, since this study employs several dynamic operators, our question is how we can decide which operators are to be applied for belief/reliability change of a judge. In order to solve these difficulties, we have implemented a computer system which provides two functions. First, the system can generate a Kripke model from a legal case. Second, the system provides an inconsistency solving algorithm which can automatically perform several operations in order to reduce the effort needed to decide which operators are to be applied. By our implementation, the above questions can be adequately solved. With our analysis method, six legal cases are analyzed to demonstrate our implementation.

## Keywords

Belief revision Reliability change Legal case Dynamic epistemic logic## References

- Aucher G, Grossi D, Herzig A, Lorini E (2009) Dynamic context logic. In: Proceedings of logic, rationality, and interaction, second international workshop, LORI 2009, Chongqing, China, 8–11 Oct 2009, pp 15–26Google Scholar
- Baltag A, van Ditmarsch HP, Moss LS (2008) Epistemic logic and information update. In: Adriaans P, van Benthem J (eds) Handbook on the philosophy of information. Elsevier, Amsterdam, pp 361–456CrossRefGoogle Scholar
- Baltag A, Bezhanishvili N, Özgün A, Smets S (2016) Justified belief and the topology of evidence. In: Proceedings of logic, language, information, and computation—23rd international workshop, WoLLIC 2016, Puebla, Mexico, 16–19th Aug 2016, pp 83–103Google Scholar
- Bench-Capon TJM, Prakken H (2008) Introducing the logic and law corner. J Log Comput 18:1–12CrossRefzbMATHGoogle Scholar
- Cadoli M, Schaerf M (1993) A survey of complexity results for nonmonotonic logics. J Log Progr 17(2–4):127–160MathSciNetCrossRefzbMATHGoogle Scholar
- Cholvy L (2005) A modal logic for reasoning with contradictory beliefs which takes into account the number and the reliability of the sources. In: Proceedings of symbolic and quantitative approaches to reasoning with uncertainty, 8th European conference, ECSQARU 2005, Barcelona, Spain, 6–8 July 2005, pp 390–401Google Scholar
- Dragoni A, Giorgini P (2001) Revising beliefs received from multiple sources. In: Williams MA, Rott H (eds) Frontiers in belief revision. Applied logic series, vol 22. Springer, Dordrecht, pp 429–442CrossRefGoogle Scholar
- Dung PM (1995) On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif Intell 77(2):321–358MathSciNetCrossRefzbMATHGoogle Scholar
- Gardenfors P (ed) (1992) Belief revision. Cambridge University Press, New YorkzbMATHGoogle Scholar
- Ghosh S, Velázquez-Quesada F (2011) Merging information. In: van Benthem J, Gupta A, Pacuit E (eds) Games, norms and reasons: logic at the crossroads,
*Synthese Library*, vol 353. Springer, BerlinGoogle Scholar - Governatori G, Rotolo A (2010) Changing legal systems: legal abrogations and annulments in defeasible logic. Log J IGPL 18(1):157–194MathSciNetCrossRefzbMATHGoogle Scholar
- Grossi D, Rotolo A (2011) Logic in the law: a concise overview. Log Philos Today Stud Log 30:251–274zbMATHGoogle Scholar
- Grossi D, Velázquez-Quesada FR (2009)
*Twelve Angry Men*: a study on the fine-grain of announcements. In: Proceedings of logic, rationality, and interaction, second international workshop, LORI 2009, Chongqing, China, 8–11 Oct 2009, pp 147–160Google Scholar - Jirakunkanok P, Hirose S, Sano K, Tojo S (2013) Belief re-revision in chivalry case. In: New frontiers in artificial intelligence—JSAI-isAI 2013 workshops, LENLS, JURISIN, MiMI, AAA, and DDS, Kanagawa, Japan, 27–28 Oct 2013, revised selected papers, pp 230–245Google Scholar
- Jirakunkanok P, Sano K, Tojo S (2014) Analyzing reliability change in legal case. In: New frontiers in artificial intelligence—JSAI-isAI 2014 workshops, LENLS, JURISIN, and GABA, Kanagawa, Japan, 27–28 Oct 2014, revised selected papers, pp 274–290Google Scholar
- Jirakunkanok P, Sano K, Tojo S (2015) Analyzing belief re-revision by consideration of reliability change in legal case. In: 2015 seventh international conference on knowledge and systems engineering, KSE 2015, Ho Chi Minh City, Vietnam, 8–10 Oct 2015, pp 228–233Google Scholar
- Jirakunkanok P, Sano K, Tojo S (2015) An implementation of belief re-revision and reliability change in legal case. In: Proceedings of the ninth international workshop of Juris-informatics, pp 97–110Google Scholar
- Jurafsky D, Martin JH (2009) Speech and language processing: an introduction to natural language processing, computational linguistics, and speech recognition, 2nd edn. Prentice Hall PTR, Upper Saddle RiverGoogle Scholar
- Kiel M (2013) Belief aggregation in multi-agent dynamic epistemic logic. Master’s thesis, Ludwig-Maximilian University of Munich, Germany (2013)Google Scholar
- Liau CJ (2003) Belief, information acquisition, and trust in multi-agent systems—a modal logic formulation. Artif Intell 149(1):31–60MathSciNetCrossRefzbMATHGoogle Scholar
- Liu F, Seligman J, Girard P (2014) Logical dynamics of belief change in the community. Synthese 191(11):2403–2431MathSciNetCrossRefzbMATHGoogle Scholar
- Liu F, Lorini E (2016) Reasons to believe in a social environment. In: International conference on deontic logic in computer science (DEON), Bayreuth, 18 July 2016–21 July 2016, College Publications, pp 155–170Google Scholar
- Lorini E, Perrussel L, Thévenin J (2011) A modal framework for relating belief and signed information. Comput Log Multi-agent Syst 6814:58–73CrossRefzbMATHGoogle Scholar
- Nute D (1994) Defeasible logic. In: Handbook of logic in artificial intelligence and logic programming: nonmonotonic reasoning and uncertain reasoning, vol 3, pp 353–395. Oxford University Press, Inc., OxfordGoogle Scholar
- Obeid N, Turner R (1991) Logical foundations of nonmonotonic reasoning. Artif Intell Rev 5(1–2):53–70CrossRefGoogle Scholar
- Perrussel L, Thévenin J (2004) (Dis)belief change based on messages processing. In: Computational logic in multi-agent systems, 4th international workshop, CLIMA IV, Fort Lauderdale, FL, USA, 6–7 Jan 2004, revised selected and invited papers, pp 201–217Google Scholar
- Prakken H (1997) Logical tools for modelling legal argument: a study of defeasible reasoning in law. Kluwer, DordrechtCrossRefGoogle Scholar
- Prakken H, Sartor G (2001) The role of logic in computational models of legal argument—a critical survey. Comput Log Log Program Beyond Lect Notes Comput Sci 2408:342–381CrossRefzbMATHGoogle Scholar
- Roorda JW, van der Hoek W, Meyer JJC (2002) Iterated belief change in multi-agent systems. In: AAMAS, ACM, pp 889–896Google Scholar
- van Benthem J, Liu F (2007) Dynamic logic of preference upgrade. J Appl Non-Class Log 17(2):157–182MathSciNetCrossRefzbMATHGoogle Scholar
- van Benthem J, Pacuit E (2011) Dynamic logics of evidence-based beliefs. Stud Log 99(1–3):61–92MathSciNetCrossRefzbMATHGoogle Scholar
- van Benthem J, van Eijck J, Gattinger M, Su K (2015) Symbolic model checking for dynamic epistemic logic. In: Proceedings of logic, rationality, and interaction—5th international workshop, LORI 2015 Taipei, Taiwan, 28–31 Oct 2015, pp 366–378Google Scholar
- van Ditmarsch H (2003) The russian cards problem. Stud Log 75(1):31–62MathSciNetCrossRefzbMATHGoogle Scholar
- van Ditmarsch HP, van der Hoek W, Kooi BP (2007) Dynamic epistemic logic and knowledge puzzles. In: Proceedings of conceptual structures: knowledge architectures for smart applications, 15th international conference on conceptual structures, ICCS 2007, Sheffield, UK, 22–27 July 2007, pp 45–58Google Scholar
- van Ditmarsch H, van der Hoek W, Kooi B (2008) Dynamic epistemic logic. Springer, BerlinzbMATHGoogle Scholar
- van Ditmarsch H, van Eijck J, Hernández-Antón I, Sietsma F, Simon S, Soler-Toscano F (2012) Modelling cryptographic keys in dynamic epistemic logic with DEMO. In: Highlights on practical applications of agents and multi-agent systems - 10th international conference on practical applications of agents and multi-agent systems, PAAMS 2012 special sessions, Salamanca, Spain, 28–30 Mar 2012, pp 155–162Google Scholar
- Velázquez-Quesada FR (2014) Dynamic epistemic logic for implicit and explicit beliefs. J Log Lang Inf 23(2):107–140MathSciNetCrossRefzbMATHGoogle Scholar