Contrary to time conditionals in Talmudic logic

We consider conditionals of the form A ? B where A depends on the future and B on the present and past. We examine models for such conditional arising in Talmudic legal cases. We call such conditionals contrary to time conditionals. Three main aspects will be investigated:

1. Inverse causality from future to past, where a future condition can influence a legal event in the past (this is a man made causality).
2. Comparison with similar features in modern law.
3. New types of temporal logics arising from modelling the Talmudic examples.

We shall see that we need a new temporal logic,which we call Talmudic temporal logic with linear open advancing future and parallel changing past, based on two parameters for time.     

Moral particularism in the light of deontic logic

The aim of this paper is to strengthen the point made by Horty about the relationship between reason holism and moral particularism. In the literature prima facie obligations have been considered as the only source of reason holism. I strengthen Horty??s point in two ways. First, I show that contrary-to-duties provide another independent support for reason holism. Next I outline a formal theory that is able to capture these two sources of holism. While in simple settings the proposed account coincides with Horty??s one, this is not true in more complicated or ??realistic?? settings in which more than two norms collide. My chosen formalism is so-called input/output logic. A bottom-line example is introduced. It raises the issue of whether the conventional wisdom is right in assuming that normative reasons run parallel to epistemic ones.     

Conditional obligation,deontic paradoxes,and the logic of agency

A variant of Belnap's stit-semantics due to Horty and von Kutschera is used to develop a semantics of obligation. A partial completeness result is stated. The semantics is then used to discuss conditional obligation as well as two paradoxes of deontic logic. The paper argues for the importance of an analysis of agency for deontic logic.     

Utilizing deontic operators in information systems specification

One major task in requirements specification is to capture the rules relevant to the problem at hand. Declarative, rule-based approaches have been suggested by many researchers in the field. However, when it comes to modeling large systems of rules, not only for the behavior of the computer system but also for the organizational environment surrounding it, current approaches have problems with limited expressiveness, flexibility, and poor comprehensibility. Hence, rule-based approaches may benefit from improvements in two directions: (1) improvement of the rule languages themselves and (2) better integration with other, complementary modeling approaches.In this article, both issues are addressed in an integrated manner. The proposal is presented in the context of the Tempora project on rule-based information systems development, but has also been integrated with PPP. Tempora has provided a rule language based on an executable temporal logic working on top of a temporal database. The rule language is integrated with static (ER-like) and dynamic (SA/RT-like) modeling approaches. In the current proposal, the integration with complementary modeling approaches is extended by including organization modeling (actors, roles), and the expressiveness of the rule language is increased by introducing deontic operators and rule hierarchies. The main contribution of the article is not seen as any one of the above-mentioned extensions, but as the resulting comprehensive modeling support. The approach is illustrated by examples taken from an industrial case study done in connection with Tempora.C. List of Symbols Subset of set - Not subset of set - Element of set - Not element of set - Equivalent to - Not equivalent to - ¬ Negation - Logical and - Logical or - Implication - Sometime in past - Sometime in future - Always in past - Always in future - Just before - Just after - u Until - s Since - Trigger - Condition - _s State condition - Consequence - _a Action - _s State - Role - Actor - ¬ - General deontic operator - O Obligatory - R Recommended - P Permitted - D Discouraged - F Forbidden - (/–) General rule - t _R Real time - t _M Model time     

Effective algorithms for games with prohibitions and their applications

In this paper, a polynomial algorithm of solving games with prohibitions with a uniform functional over a loop for strongly ergodic game networks. We give the criterion of strong ergodicity of a simple network and show that the definition of strong ergodicity is a co-NP-complete problem. The games with prohibitions are interpreted in the context of problems of scheduling theory with logical conditions of preceding.     

Provisions and Obligations in Policy Rule Management

Policies in modern systems and applications play an essential role. We argue that decisions based on policy rules should take into account the possibility for the users to enable specific policy rules, by performing actions at the time when decisions are being rendered, and/or by promising to perform other actions in the future. Decisions should also consider preferences among different sets of actions enabling different rules. We adopt a formalism and mechanism devised for policy rule management in this context, and investigate in detail the notion of obligations, which are those actions users promise to perform in the future upon firing of a specific policy rule. We also investigate how obligations can be monitored and how the policy rules should be affected when obligations are either fulfilled or defaulted.     

概率逻辑、不确定逻辑和模糊逻辑之比较

通过一个实例分析比较了概率逻辑、主观概率逻辑、不确定逻辑和模糊逻辑的思想方法。提出了自己的观点：基于数据统计的概率逻辑是最科学的。不确定逻辑比主观概率逻辑更科学。当具有不确定性的原子命题具有独立性时,不确定逻辑和模糊逻辑的观点是一致的。而对于处理带有不确定性的相关性命题,不确定逻辑比模糊逻辑更科学。但是模糊逻辑在建立推理理论方面见长。     

二值命题逻辑中逻辑理论的计量化及应用

在二值命题逻辑系统中,利用势为2的均匀概率测度空间的无穷乘积,通过计算理论[Γ]的全体模型占整个赋值空间的测度定义了理论[Γ]的真度,进而利用理论的真度简化了理论的发散度和相容度的计算公式,给出了由推理的前提集的真度估计其逻辑结论真度的表达式。     

Multiple-valued logic and optimization of programmable logic arrays

Shows a method of designing programmable logic arrays (PLAs) using multiple-valued input, two-valued output functions (MVITVOFs). A MVITVOF is an extension of the two-valued logic function. An expression for a MVITVOF directly represents a multiple-output PLA with decoders. Each product of the expression corresponds to each column of the PLA, so the number of products; in the expression equals the number of columns of the PLA. The array size of the PLA is proportional to the number of products; the PLA can thus be minimized by minimizing the expression     

The logic of optics and the optics of logic

There have been various attempts to implement the standard logical formalism, known as “Boolean Logic”, stemming from Aristotle, the Stoics, Leibniz, Boole, and Frege, extending to the fuzzy logic developed by Zadeh [Info. Ctl. 338 (1965) 353]. That logic, isomorphic, as we now know, with the logic of electric circuitry, was not designed for optical implementation. Nor has there been a notable success in developing such an implementation. We demonstrate a new type of logic designed for implementation by coherent optics. It has the logic of Zadeh as a special case just as Zadeh's logic has the logic of Boolean algebra as a special case. Because the new logic operates over a finite set of vectors in the complex domain, we call it Vector Logic. Some Vector Logic operations are very easy to implement, but the universal “Vector NOR” or VNOR gate is quite complex. Optical Vector Logic gates are passive, so they operate at the bandwidth of the signal input and readout. And, of course, the parallel nature of many coherent optical processors can apply here as well to yield SIMD and even MIMD systems.     

经典逻辑公理在模糊逻辑系统中的真度分析

对经典逻辑中的公理在Gödel系统、Lukasiewicz以及R₀系统中的真度大小进行了分析,得到了一系列深刻而有趣的结果。     

How much logic should go in an FPGA logic block

The logic blocks of most FPGAs contain clusters of lookup tables and flip-flops yet little is known about good choices for key parameters. How many lookup tables should a cluster contain, how should FPGA routing flexibility change as cluster size changes, and how many inputs should programmable routing provide each cluster?     

Completeness of a combination of neighbourhood logic and temporal logic

This paper presents a completeness result, with respect to a possible world semantics, for a combination of a first-order temporal logic and neighbourhood logic. This logic was considered by Qiu and Zhou (1998, Proceedings of the PROCOMET 98, pp 444–461) to define semantics of a real-time OCCAM-like programming language.Received June 1999Accepted in revised form September 2003 by M. R. Hansen and C. B. Jones     

Jumps and logic in the law

The main stream of legal theory tends to incorporate unwritten principles into the law. Weighing of principles plays a great role in legal argumentation, inter alia in statutory interpretation. A weighing and balancing of principles and other prima facie reasons is a jump. The inference is not conclusive.To deal with defeasibility and weighing, a jurist needs both the belief-revision logic and the nonmonotonic logic. The systems of nonmonotonic logic included in the present volume provide logical tools enabling one to speak precisely about various kinds of rules about rules, dealing with such things as applicability of rules, what is assumed by rules, priority between rules and the burden of proof. Nonmonotonic logic is an example of an extension of the domain of logic. But the more far-reaching the extension is, the greater problems it meets. It seems impossible to make logical reconstruction of the totality of legal argumentation.The lawyers' search for reasons has no obvious end point. Ideally, the search for reasons may end when one arrives at a coherent totality of knowledge. In other words, coherence is the termination condition of reasoning. Both scientific knowledge and knowledge of legal and moral norms progresses by trial and error, and that one must resort to a certain convention to define what error means. The main difference is, however, that conventions of science are much more precise than those of legal scholarship.Consequently, determination of error in legal science is often holistic and circular. The reasons determining that a legal theory is erroneous are not more certain than the contested theory itself. A strict and formal logical analysis cannot give us the full grasp of legal rationality. A weaker logical theory, allowing for nonmonotonic steps, comes closer, at the expense of an inevitable loss of computational efficiency. Coherentist epistemology grasps even more of this rationality, at the expense of a loss of preciseness.     

Modularization and abstraction in logic programming

In knowledge information processing, the structuring of knowledge and algorithms is one of the key issues. The goal of this work is to introduce the concepts and mechanisms of abstraction, modularization and parameterization into logic programming, which is one of the preliminary steps toward creating a kernel language for fifth generation computer systems.     

Persistence and minimality in epistemic logic

We give a general approach to characterizing minimal information in a modal context. Our modal treatment can be used for many applications, but is especially relevant under epistemic interpretations of the operator □. Relative to an arbitrary modal system, we give three characterizations of minimal information and provide conditions under which these characterizations are equivalent. We then study information orders based on bisimulations and Ehrenfeucht–Fraïssé games. Moving to the area of epistemic logics, we show that for one of these orders almost all systems trivialize the notion of minimal information. Another order which we present is much more promising as it permits to minimize with respect to positive knowledge. In S5, the resulting notion of minimal knowledge coincides with well‐established proposals. For S4 we compare the two orders.