This paper examines the deontic logic of the Talmud. We shall find, by looking at examples, that at first approximation we need deontic logic with several connectives: O T A Talmudic obligation F T A Talmudic prohibition F D A Standard deontic prohibition O D A Standard deontic obligation. In classical logic one would have expected that deontic obligation O D is definable by $O_DA \equiv F_D\neg A$ and that O T and F T are connected by $O_TA \equiv F_T\neg (...) A$ This is not the case in the Talmud for the T (Talmudic) operators, though it does hold for the D operators. We must change our underlying logic. We have to regard {O T , F T } and {O D , F D } as two sets of operators, where O T and F T are independent of one another and where we have some connections between the two sets. We shall list the types of obligation patterns appearing in the Talmud and develop an intuitionistic deontic logic to accommodate them. We shall compare Talmudic deontic logic with modern deontic logic. (shrink)

Given an argumentation network we associate with it a modal formula representing the ‘logical content’ of the network. We show a one-to-one correspondence between all possible complete Caminada labellings of the network and all possible models of the formula.

The extremely successful _Standard Model of Particle Physics_ allows one to define the so-called _Elementary Particles_. From another point of view, how can we think of them? What kind of a status can be attributed to Elementary Particles and their associated quantised fields? Beyond the unprecedented efficiency and reach of quantum field theories, the current paper attempts at understanding the nature of what these theories describe, the enigmatic reality of the quantum world.

An ontology of geographic kinds is designed to yield a better understanding of the structure of the geographic world, and to support the development of geographic information systems that are conceptually sound. This paper first demonstrates that geographical objects and kinds are not just larger versions of the everyday objects and kinds previously studied in cognitive science. Geographic objects are not merely located in space, as are the manipulable objects of table-top space. Rather, they are tied intrinsically to space, and (...) this means that their spatial boundaries are in many cases the most salient features for categorization. The ontology presented here will accordingly be based on topology (the theory of boundary, contact and separation) and on mereology (the theory of extended wholes and parts). Geographic reality comprehends mesoscopic entities, many of which are best viewed as shadows cast onto the spatial plane by human reasoning and language. Because of this, geographic categories are much more likely to show cultural differences in category definitions than are the manipulable objects of table-top space. (shrink)

Dr. Jameson's editio princeps of his major discovery at Troizen will long remain essential for the study of this document. The following jottings are largely footnotes to the rich material which he has collected. Their main preoccupation is linguistic, and I abstain from any attempt to fit the decree into its historical setting. The gap between 480 B.C. and our copy is so long that it is hardly to be expected that the authenticity of the decree will go unchallenged, and (...) this exploration of some points in the language may help towards a decision. (shrink)

There are several areas in applied logic where deletion from databases is involved in one way or another:Belief contraction Triggers of the form ‘If condition then remove A’, which are extensively used in database management systemsResource considerations as in relevance and linear logics, where addition or removal of resource can affect provabilityFree logic and the like, where existence and non-existence of individuals affects quantification.All of these areas have certain logical difficulties relating to the removal of elements. This paper points out (...) the difficulties and offers a comprehensive logical model. (shrink)

We introduce reactive Kripke models for intuitionistic logic and show that the reactive semantics is stronger than the ordinary semantics. We develop Beth tableaux for the reactive semantics.

This chapter contains sections titled: Labeled Deductive Systems in Context Examples from Monotonic Logics Examples from Non‐monotonic Logics Conclusion and Further Reading.