Variable Priorities and Exclusionary Reasons in Input/Output Logic

Jörg Hansen, John Horty, and Xavier Parent and Leendert van der Torre have all recently described some sort of nonmonotonic logic to model reasons and their interactions. Horty’s framework is broader in scope than the other two, encompassing both reasoning about the relative strengths of reasons and reasoning about which reasons to consider in the first place. Hansen discusses a plethora of approaches and examples, including Horty’s, arguing that his preferred system best captures our intuitions. And Parent and van der Torre present a family of systems of input/output logic, which are in some ways the most flexible. In this paper, I aim to combine these features. Without attempting to answer the question of which intuitions are the best to capture, I first argue that there are good reasons to explore systems that behave more like Hansen’s than Horty’s. I then show that Parent and van der Torre’s framework of input/output logic can exactly duplicate Hansen’s system but is flexible enough to produce other results as well. Finally, I extend their framework to include the additional kinds of reasoning Horty discusses, showing that the resulting theory can handle a wider range of cases than Horty’s.     

Input/Output Logics

In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. Our purpose is to develop a theory of such input/output operations. Four are singled out: simple-minded, basic (making intelligent use of disjunctive inputs), simple-minded reusable (in which outputs may be recycled as inputs), and basic reusable. They are defined semantically and characterised by derivation rules, as well as in terms of relabeling procedures and modal operators. Their behaviour is studied on both semantic and syntactic levels.     

Constraints for Input/Output Logics

In a previous paper we developed a general theory of input/output logics. These are operations resembling inference, but where inputs need not be included among outputs, and outputs need not be reusable as inputs. In the present paper we study what happens when they are constrained to render output consistent with input. This is of interest for deontic logic, where it provides a manner of handling contrary-to-duty obligations. Our procedure is to constrain the set of generators of the input/output system, considering only the maximal subsets that do not yield output conflicting with a given input. When inputs are authorised to reappear as outputs, both maxichoice revision in the sense of Alchourrón/Makinson and the default logic of Poole emerge as special cases, and there is a close relation with Reiter default logic. However, our focus is on the general case where inputs need not be outputs. We show in what contexts the consistency of input with output may be reduced to its consistency with a truth-functional combination of components of generators, and under what conditions constrained output may be obtained by a derivation that is constrained at every step.     

Permission from an Input/Output Perspective

Input/output logics are abstract structures designed to represent conditional obligations and goals. In this paper we use them to study conditional permission. This perspective provides a clear separation of the familiar notion of negative permission from the more elusive one of positive permission. Moreover, it reveals that there are at least two kinds of positive permission. Although indistinguishable in the unconditional case, they are quite different in conditional contexts. One of them, which we call static positive permission, guides the citizen and law enforcement authorities in the assessment of specific actions under current norms, and it behaves like a weakened obligation. Another, which we call dynamic positive permission, guides the legislator. It describes the limits on the prohibitions that may be introduced into a code, and under suitable conditions behaves like a strengthened negative permission.     

Characterizations of Negative Definability in Modal Logic

Negative definability ([18]) is an alternative way of defining classes of Kripke frames via a modal language, one that enables us, for instance, to define the class of irreflexive frames. Besides a list of closure conditions for negatively definable classes, the paper contains two main theorems. First, a characterization is given of negatively definable classes of (rooted) finite transitive Kripke frames and of such classes defined using both traditional (positive) and negative definitions. Second, we characterize the negatively definable classes of rooted general frames.     

Adaptive Logic as a Modal Logic

Modal logics have in the past been used as a unifying framework for the minimality semantics used in defeasible inference, conditional logic, and belief revision. The main aim of the present paper is to add adaptive logics, a general framework for a wide range of defeasible reasoning forms developed by Diderik Batens and his co-workers, to the growing list of formalisms that can be studied with the tools and methods of contemporary modal logic. By characterising the class of abnormality models, this aim is achieved at the level of the model-theory. By proposing formulae that express the consequence relation of adaptive logic in the object-language, the same aim is also partially achieved at the syntactical level.     

A convenient and accurate parallel Input/Output USB device for E-Prime

Psychological and neurophysiological experiments require the accurate control of timing and synchrony for Input/Output signals. For instance, a typical Event-Related Potential (ERP) study requires an extremely accurate synchronization of stimulus delivery with recordings. This is typically done via computer software such as E-Prime, and fast communications are typically assured by the Parallel Port (PP). However, the PP is an old and disappearing technology that, for example, is no longer available on portable computers. Here we propose a convenient USB device enabling parallel I/O capabilities. We tested this device against the PP on both a desktop and a laptop machine in different stress tests. Our data demonstrate the accuracy of our system, which suggests that it may be a good substitute for the PP with E-Prime.     

The Adaptive Logic of Compatibility

This paper describes the adaptive logic of compatibility and its dynamic proof theory. The results derive from insights in inconsistency-adaptive logic, but are themselves very simple and philosophically unobjectionable. In the absence of a positive test, dynamic proof theories lead, in the long run, to correct results and, in the short run, sometimes to final decisions but always to sensible estimates. The paper contains a new and natural kind of semantics for S5from which it follows that a specific subset of the standard worlds-models is characteristic for S5.     

The Undecidability of Propositional Adaptive Logic

We investigate and classify the notion of final derivability of two basic inconsistency-adaptive logics. Specifically, the maximal complexity of the set of final consequences of decidable sets of premises formulated in the language of propositional logic is described. Our results show that taking the consequences of a decidable propositional theory is a complicated operation. The set of final consequences according to either the Reliability Calculus or the Minimal Abnormality Calculus of a decidable propositional premise set is in general undecidable, and can be -complete. These classifications are exact. For first order theories even finite sets of premises can generate such consequence sets in either calculus.     

Correlations Between Input and Output Units in Neural Networks

Correlation analyses of recent back-propagation neural networks show that network results are due to imbalances in stimulus input. Conclusions concerning the effects of receptive field size, hemispheric specialization, and other issues of relevance to psychology cannot therefore be drawn until the dominating effects of low-level correlations are removed. Statistical techniques for evaluating the stimulus materials for neural networks are introduced.     

Input/output switch in bilingual code switching

Chinese-English bilinguals were asked to read a passage with spontaneous bilingual code switchings, compared with a unilingual Chinese translation of the passage, a unilingual English translation, a translation with random switchings, and a translation with only nouns switched into English. There was no difference between the reading speed for the passage with natural switchings and the unilingual Chinese passage, thus questioning the need to postulate a bilingual imput/output switch. The speed for reading passages with artificial switchings was slower. In a translation task, the naturally switched items required less time in Chinese-to-English translations compared with English-to-Chinese translations. This indicates that in natural code switchings, the English lexical items produced were more available, even though English is generally the weaker language.     

Logic and Philosophy of Logic in Wittgenstein

This essay discusses Wittgenstein's conception of logic, early and late, and some of the types of logical system that he constructed. The essay shows that the common view according to which Wittgenstein had stopped engaging in logic as a philosophical discipline by the time of writing Philosophical Investigations is mistaken. It is argued that, on the contrary, logic continued to figure at the very heart of later Wittgenstein's philosophy; and that Wittgenstein's mature philosophy of logic contains many interesting thoughts that have gone widely unnoticed.     

Algebraic Characterizations of Various Beth Definability Properties

In this paper it will be shown that the Beth definability property corresponds to surjectiveness of epimorphisms in abstract algebraic logic. This generalizes a result by I. Németi (cf. [11, Theorem 5.6.10]). Moreover, an equally general characterization of the weak Beth property will be given. This gives a solution to Problem 14 in [20]. Finally, the characterization of the projective Beth property for varieties of modal algebras by L. Maksimova (see [15]) will be shown to hold for the larger class of semantically algebraizable logics.     

Quantum Logic as a Fragment of Independence-Friendly Logic

The working assumption of this paper is that noncommuting variables are irreducibly interdependent. The logic of such dependence relations is the author's independence-friendly (IF) logic, extended by adding to it sentence-initial contradictory negation ¬ over and above the dual (strong) negation . Then in a Hilbert space turns out to express orthocomplementation. This can be extended to any logical space, which makes it possible to define the dimension of a logical space. The received Birkhoff and von Neumann quantum logic can be interpreted by taking their disjunction to be ¬(A & B). Their logic can thus be mapped into a Boolean structure to which an additional operator has been added.     

图式逻辑:哲学逻辑的一个新分支

逻辑研究有效推理,判定其有效的依据是结论所传达的信息与前提所传达的信息之间的必然关系,而传达这些信息的媒介不一定就是语言。日常推理是运用语句、图形甚至声音、气味等多种信息进行的多模态推理,对这些多模态表示系统和推理的研究已经成为心灵哲学、认知科学、心理学、教育学、数学、逻辑学和计算机科学等领域的交叉地带。自从     

从劳动逻辑到实践逻辑

马克思实践哲学面临了从劳动逻辑向实践逻辑提升和转换的需要,以拯救易被化约于"劳动"之中的伦理—政治型"实践"范畴的独立地位。但这项工作必须自觉区别于西方实践哲学传统的"实践"与"劳动"二分立场。马克思劳动概念中蕴含了属于它自身的伦理规范内涵,需要将这一伦理规范内涵释放出来,以完成向伦理—政治型实践范畴的过渡。