CTD Paradox Research

What deontic logic research is "must", "permir", "forbid" and so on moral concepts as well as proposition inference form related with these concept. In 1951, Von Wright published an article ,"Deontic Logic", in magazine "Mind", which was considered the first feasible deontic logic system. Now what the people widely use is the SDL system (standard deontic logic system), but the SDL system receives a series of paradoxes,in which most lets the logician headache is the CTD paradox. The CTD paradox is the abbreviation of contrary-to-duty paradox. The CTD paradox discussed here is a series of similar paradox's general name. Chisholm( R. M. chisholm) paradox (also said that "Chisholm delimma") is a CTD paradox which proposed firstly. in 1963 Chisholm in an article proposed four natural sentences in " Contrary-to-duty And Deontic Logic". Chisholm's four natural are conincident, moreover between the sentence does not have the independence intuitively.But even we exhaust all possible way in the SDL system, we are not able to discover the satisfying method, either lacks the independence, either in the intuition has in the contradiction or the intuition and formally has the contradiction. After Chisholm, also many scholars propose many similar paradoxes. Their paradoxes equally are unable in the SDL system to obtain the appropriate form portray with Chisholm's .Deontic logic research both has the significant theory significance, and has the important practice significance, because the CTD duty is the judicial inference and the daily moral inference must appear surely. The author thought that the CTD paradox's appear has the following two aspects: SDL takes the vera modal logic as a foundation, and constructs system through expansion.Also,the vera modal logic also expands in the classical logic foundation. Therefore, these theorem which counteracted to the common sense in the vera modal logic and in the classical logic system in the has been inherited by SDL. This is also the reason which actually produces other deontic logical paradox. On the other hand, the CTD paradox produces to the CTD duty form formal portray. The SDL system does not have ability to carry on the appropriate portray to the CTD duty. This is the CTD paradox unique question, therefore solves the CTD paradox primary mission lies in finding the appropriate form portray of the CTD duty. This article will use three methods to its formalization.The first method is the dual deontic logic method. Along with to the deontic logic's deep research, the dual deontic logical system produced. Who firstly establishes the dual deontic logical system are Von Wright and N.Rescher. The original intention of their establishment of the dual deontic logical system lies in eliminate the paradoxes in monadic deontic logic, particularly CTD paradoxes. Henry Prakken and Marek Sergot also attempt to use the dual deontic logical system to eliminate these paradoxes. This method solution paradoxes' basic concept is the discrimination initial level duty and the CTD level duty as well as the different level CTD duty, and proved that so-called counteracted the sentences are in the different levels, between them will not have the contradiction. Although this method satisfis the eight requests, proposed by J.Carmo and A.J.I.Jones, which must satisfy, but cannot satisfy the fourth one, will have some flaws.The second method is the method in which deontic logic connects tense logic. Generally, the duty being, changing, vanishing unceasingly because of the time changing, therefore the time is an important attribute in the moral inference and the judicial inference actually,therefore it meets the actual need that introducing tense factor in deontic logic's frame. Deontic logic and the tense logic's union, has become one kind of new tendency in structuring deontic logical systems. But the tense deontic logic this article uses is one kind of "the camouflage" tense deontic logic, tense concept here has not any special function, but it actually has made the quite reasonable form to portray the CTD paradox. This method' difference to the Henry Prakken and Marek Sergot's lies in: First it has introduced deontic order, which can define the initial duty and the condition duty well; Next has rejected deontic separation rule and the condition duty separation rule, which causes in the system to avoid presenting more initial duties; How did it become the CTD duty to the condition duty to carry on the appropriate definition once more. This method has satisfied satisfis the eight requests, proposed by J.Carmo and A.J.I.Jones, especially,the fourth one.The third method is the situation calculus method. Recent year the logical world also has one kind of tendency, namely does not take deontic logic as a branch of the modal logic, and logicians do not use the research technique of the logic modal to study deontic logic. This article will introduce that one kind that processes the CTD paradoxes with the situation calculus . This basic idea of this method to solves the CTD paradoxes is: First form the natural sentence, Using SDL to form Chisholm paradoxes, four sentences does not have situation factor,while forming them with the situation calculus,we must pay attention to first three involving deontic concept is under all situations, but the one which expressing the fact only occurs under the special situation; Next, the establish initial setting which conforms to the formed sentence. Once more, the establish successor condition axiom and deontic successor condition axiom which conforms to the formalized sentence; Finally, prove that the conflicting duties are not under the identical situation. This method is one very easy inference method, it has satisfied J.Carmo and A.J.I.Jones 'eight requests. In addition, it does not use the possible world semantics, therefore it may avoid the trouble which to bring with the possible world semantics.My work in this paper is the analysis each method in detail, and attempt processing all CTD paradoxes, finally comment them.