Reasoning with dimensions and magnitudes

  title={Reasoning with dimensions and magnitudes},
  author={John F. Horty},
  journal={Artificial Intelligence and Law},
  • J. Horty
  • Published 12 June 2017
  • Computer Science
  • Artificial Intelligence and Law
This paper shows how two models of precedential constraint can be broadened to include legal information represented through dimensions. I begin by describing a standard representation of legal cases based on boolean factors alone, and then reviewing two models of constraint developed within this standard setting. The first is the “result model”, supporting only a fortiori reasoning. The second is the “reason model”, supporting a richer notion of constraint, since it allows the reasons behind a… 
Precedential constraint: the role of issues
It is argued that problems arise from ignoring the structure of legal cases that is provided by the notion of issues, and that seeing precedential constraint in terms of issues rather than whole cases provides a more effective approach and better reflects legal practice.
Dimensions and Values for Reasoning with Legal Cases
The link between dimensions and values is revisited, showing that values play a number of distinct roles, not only explaining preferences between factors, but also ensuring that all the purposes of the underlying law are considered.
Modifying the reason model
  • J. Horty
  • Computer Science
    Artif. Intell. Law
  • 2021
The purpose of this note is to suggest a modification of the reason model of constraint that distinguishes it from the result model even in the dimensional setting.
The link between dimensions and values is revisited, arguing that values play a number of distinct roles, not only explaining preferences between factors, but also ensuring that all the purposes of the underlying law are considered.
Reasoning with Legal Cases: Analogy or Rule Application?
It is suggested that there will always be limits to the ability to construct systems able to handle new cases presenting novel situations, and theAbility to perform analogical reasoning on novel situations is, and is likely to remain, infeasible.
Comparing Alternative Factor- and Precedent-Based Accounts of Precedential Constraint
An alternative is proposed, which unlike existing models does not require that for each value assignment to a dimension it is specified whether it is for or against the case’s outcome, which arguably makes the model easier to apply in practice.
Vertical precedents in formal models of precedential constraint
It is shown that no model can capture the U.S. doctrine of precedent without making that distinction between horizontal and vertical precedents, and a precise model is developed that does just that.
ABSTRACT According to the prioritized reason model of precedent, precedential constraint is explained in terms of the need for decision-makers to reconcile their decisions with a settled priority
Representing dimensions within the reason model of precedent
This paper gives an account of dimensions in the reason model found in Horty, Horty and Bench-Capon, and Rigoni, and discusses how dimensions might be established from a case base and how dimensions that are incomplete in various aspects might be dealt with in the theory.
Dimensions and Values for Legal CBR
Dimensions and values are discussed, arguing that values can play several distinct roles, both explaining preferences between factors and indicating the purposes of the law.


A factor-based definition of precedential constraint
This paper describes one way in which a precise reason model of precedent could be developed, based on the general idea that courts are constrained to reach a decision that is consistent with the
Constraint and Freedom in the Common Law
The purpose of this paper is to advance our formal understanding of the common law, especially the nature of the reasoning involved, but also its point, or justification. As so often in discussions
Back to the Future: Dimensions Revisited
Most recent work on reasoning with cases in law has taken the style of rea- soning used in the CATO system as its model, and uses the notion of factors, as found in that system. Fundamental to CATO,
A model of legal reasoning with cases incorporating theories and values
Representing Popov v Hayashi with dimensions and factors
This paper considers how several varieties of the approach to modelling reasoning with legal cases can be applied to the interesting case of Popov v Hayashi, represented in terms of factors and dimensions.
Symbolic Logic: A Razor-Edged Tool for Drafting and Interpreting Legal Documents
It is suggested that a new approach to drafting, using certain elementary notions of symbolic logic, can go a long way towards eliminating such inadvertent ambiguity.
Modelling Reasoning with Precedents in a Formal Dialogue Game
A formal method is proposed for representing precedents and it is discussed how such representations can be used in a formally defined dialectical protocol for dispute, to provide formal foundations for certain aspects of computer programs for case-based reasoning in the legal domain.
Some observations on modelling case based reasoning with formal argument models
The modelling of case based reasoning using a formal model of argument using the approach of Prakken and Sartor as a starting point is explored, and the issues relating to quantifiable factors and factor hierarchies are considered.
The doctrine of precedent is one of the most distinctive features of the modern common law. Understanding the operation of precedent is important for our theorizing about the nature of law, since any
Interpreting statutory predicates
This paper discusses strategies that can be used to guide interpretation, particularly the interleaving of CBR and RBR, and how they are used in an agenda-based architecture, called CABARET, which is currently developing in a general way and experimenting with in the particular area of Section §280A(c)(1) of the U.S. Internal Revenue Code, which deals with the so called “home office deduction”.