Horty

Abstract： This paper discusses the logic of reason by Horty. It is worth noting that the logic of reason is not a logical system similar to moral logic， but a logical study of the concept of reason. Reason logic focuses only on how the reason supports or justifies its conclusion or action. Many philosophers， especially scholars in the field of morality， argue that the link between reason and conclusion lies in the weighing of concepts， according to which reason supports action or conclusion by providing a metaphorical weight， and that the subject should choose the one with a greater weight in the event of conflict. Horty's reasoning logic is based on his previous research on artificial intelligence and law. He understands the reason as the default premise， and the weighing concept also plays a very important role in his theory.

Keywords： Default logic， Reasons， Priority.

The introduction

Donald Davidson first proposed this concept in the field of analytical philosophy for analysis. He regarded reason as the psychological factor of the subject， which is composed of the desire and belief of the subject [1]. Horty tries to define reasons from a logical point of view， arguing that the logic of reason should be just as ordinary logic tells you how premises interact to reach a conclusion， and the logic of a reason at least tells you how the reasons interact to support the conclusion.

Horty's theory， which is the default logic that emerged and developed from Wright. His ideas emerged from the default reasoning developed in computer science and applied to moral logic and legal reasoning as well as to epistemology. This article will focus on Horty's reasoning logic system as the default， and point out the problems that still need to be explained and solved in his system.

1.The introduction of Horty's reason

The conception of reasons has been a result is discussion subject of the legal science philosophy， logic， in recent years， many about the document of reasons are mainly concentrated in the study of these similar problems， for example， the relationship between the reason and motivation， desire and values， about the reason of internal and external problems in the theory. Horty is focused on a different issue： what the reasons are， and how they support action or conclusion.

Based on Wright's default theory， Horty established his analysis of reasons [3]. On this default rule， will be the default as an arrow. According to this theory， if is the default A and B， then the Premise （） = {A}， and Conclusion （） = {B}.If S is a set of default， then the Premise （S） = {Premise （）； ∈ S} is the default set S premise in the set， and the Conclusion （S） = {Conclusion （）； ∈ S} is the default concentrated set of conclusions.

Horty gives default priority， which means that some defaults take precedence over others.If two propositions are the default， we can say that A proposition is greater than B proposition to indicate that A proposition has a higher priority， in this case， it is called A stronger than B， and Horty defines this sort relation as a strict partial order relation， and has the characteristics of anti-reflexivity and transitivity.

After， Horty Defines a certain with the default theory of priority， a certain has the priority of the default theory is a triple W， D， ， W represents the truth sets， D is the default set of symbols said strict partial order relation. A default theory based W， D， script is a subset of the default theory， D.

But most such extension information is invalid， such as the aforementioned example， assume that the default theory is that if cui di is a bird， Tweety would fly， as well as a fact， Tweety is not a bird， so the logic of this collection closure structure is {Tweety is not a bird， Tweety can fly}， this is a useless， because it is not out of any conclusions. Horty points out that only those that are triggered are effective extensions. Horty's default is applicable to a particular scenario， which means that if in that default script its premises are embedded in the conclusion and combined with the facts， the default is a triggered default. Horty defines reason as the premise that triggers the default， so cuddy is the reason a bird can be believed to be able to fly.

But reasons can conflict with each other， and a subject may have some reason to do it， and some reason not to do it. In Horty's theory， if the subject has denied this conclusion， then it will be the default said as Conflicted by default， if a script has inspired a conclusion stronger default and conflict， and this is the default Binding， then the default is Defeated in a script the Binding the default refers to the default neither conflict nor is defeated.

A stable script based on the default theory only contains the default of the binding. The correct extension E based on the default theory is based on the arbitrary stable script of the theory， and the correct extension of the default theory is based on the correct script of the theory. A proper extension extends the fact by using and only using the defaults of bindings， which refer to those that are triggered， but neither conflict nor defeat.

2. Several types of reasons for being defeated

According to the definition of "rebuttal" defeat， a default that supports a conclusion is defeated by a stronger default that supports a conflicting conclusion.In addition， Horty Also proposed another defeat form， according to the form of a second defeat， as a support the conclusion of the default defeated by another default， not because it supports the conclusion of the conflict， but because it challenges the premise and the connection between the original default， in about the document of cognitive reason， this form of defeated the known as "weakening".

In addition to the " undercutting" defeat， Raz has come up with a very close form of defeat， which is called the "exclusive" defeat.In one classic case Raz cited， Colin had to choose between sending his son to a private school and sending him to a public school.On the one hand， private schools will provide better education for Colin's son， and on the other hand， private schools will provide Colin's son with more friends. On the other hand， private schools are expensive.The two sides that support sending sons to public schools and supporting sons to private schools are conflicted， or at least one will weaken the other.However， Raz made the assumption that， in addition to these original arguments for or against， Colin had promised his wife that he would consider only those arguments directly related to his son's interests when it came to his son education.Raz argues that the commitment cannot be seen as yet another reason to support his son's decision to go to a private school， and instead it must be seen as a reason for an entirely different view - a "second-order" reason that sends out all "first-order" reasons that are irrelevant to Colin's son's interests.

In explaining the relationship between the "rebuttal" defeat and the "exclusionary" defeat or the "undercutting" defeat， Pollock believes that the latter two defeat forms should be assumed to be the same as the "rebuttal" defeat， a separate， original defeat form for analysis.But Horty thinks the analysis of the debilitating defeat that introduces priority rules is a special priority adjustment.The basic idea is that in prioritization， you assume certain values as a threshold， and Horty sets that only the defaults of those priorities above the threshold are safe defaults， and when an inferential conclusion is below the threshold， the defaults are weakened.

3 summary

Horty's reason logic reconstructs the concept of reason， which not only has an important influence in the field of artificial intelligence and law， but also has a great significance in the discussion of analytical philosophy on the concept of reason.But there are still problems， and they have not been solved.One of the questions is whether a justification for a particular action or conclusion can be countered by a weaker one.According to Horty， a reason can be defeated by a stronger reason， but he does not explain why the weakened side is stronger than the weakened side， and explains the subject's intuition in a vague way.Although this problem is a relatively small one and technical， it is indeed a detailed problem that must be solved in the logic of reason.

Reference

[1] Davidson， D.， 1963， Actions， Reasons， and Causes. In Essays on Actions and Events. New York： Clarendon Press.

[2] Joseph Raz. Reasons：Explanatory and normative New Essays on the Explanation of Action.（2009）：1-24

[3] Horty J F. Reasons as Defaults[J]. Philosophers Imprint， 2007， 7（3）.

[4] Reiter R. A logic for default reasoning[J]. Artificial Intelligence， 1987， 13（1）：81-132.

[5] Nair， Gopal Shyam， and J. Horty. "The logic of reasons." （2016）.

[6] Bonevac D. Defaulting on Reasons[J]. No?s， 2016（1）.

[7] Horty J F. Reasons and precedent[C]// The， International Conference on Artificial Intelligence and Law， Proceedings of the Conference， June 6-10， 2011， Pittsburgh， Pa， Usa. DBLP， 2011：41-50.

作者簡介：熊霓（1995，11-）女，汉族，江西，中南财经政法大学2016级硕士研究生，研究方向：法律逻辑、分析哲学。