What is the rational response when confronted with a set of propositions each of which we have some reason to accept, and yet which taken together form an inconsistent class? This was, in a nutshell, the problem addressed by the Jaina logicians of classical India, and the solution they gave is, I think, of great interest, both for what it tells us about the relationship between rationality and consistency, and for what we can learn about the logical basis of philosophical (...) pluralism. The Jainas claim that we can continue to reason in spite of the presence of inconsistencies, and indeed construct a many-valued logical system tailored to the purpose. My aim in this paper is to offer a new interpretation of that system and to try to draw out some of its philosophical implications. (shrink)

For Jizang (549−623), a prominent philosophical exponent of Chinese Madhyamaka, all things are empty of determinate form or nature. Given anything X, no linguistic item can truly and conclusively be applied to X in the sense of positing a determinate form or nature therein. This philosophy of ontic indeterminacy is connected closely with his notion of the Way (dao), which seems to indicate a kind of ineffable principle of reality. However, Jizang also equates the Way with nonacquisition as a conscious (...) state of freedom from any attachment and definite understanding whatsoever. The issue then becomes pressing as to how we are to understand Jizang's notion of the Way. Does it indicate some metaphysical principle or reality? Is it actually a skilful expedient to lead one to the consummate state of complete spiritual freedom? How is this issue related to Jizang's conception of ontic indeterminacy? In this book chapter, I examine Jizang's key writings in an attempt to clarify his ontological position. (shrink)

The work of Hugh MacColl (1837–1909) suffered the same fate after his death as before it:despite being vaguely alluded to and in part even commended, on the whole it has remained an unknown quantity. Even worse, those of his ideas which have played a decisive role in the history of logic have been credited to his successors; this is especially the case with the definition of strict implication and the first formal development of formal modal logic. This paper takes an (...) initial step towards a rectification of this unfortunate misrepresentation, presenting a bibliography of MacColl’s most significant publications with particular regard to their reception. (shrink)

When the original Dutch version of this book was presented in 1971 to the University of Leiden as a thesis for the Doctorate in philosophy, I was prevented by the academic mores of that university from expressing my sincere thanks to three members of the Philosophical Faculty for their support of and interest in my pursuits. I take the liberty of doing so now, two and a half years later. First and foremost I want to thank Professor G. Nuchelmans warmly (...) for his expert guidance of my research. A number of my most im portant sources were brought to my attention by him. During the whole process of composing this book his criticism and encouragement were carried out in a truly academic spirit. He thereby provided working conditions that are a sine qua non for every author who is attempting to approach controversial matters in a scientific manner, conditions which, however, were not easily available at that time. In a later phase I also came into contact with Professors L. M. de Rijk and J. B. Ubbink, with both of whom I had highly stimulating discussions and exchanges of ideas. The present edition contains some entirely new sections, viz. 1-9, IV-29, V-9, V-20, VII-14 (iii), (iv), VII-17 (i), VIII-22, IX-17, IX-19, X-9 and XI-8. Section X-9 was inspired by a remark made by Professor A. (shrink)

The article demonstrates that to describe the property of atomicity of transactions in database systems, we need a three-valued logic with propositional connective characterized in the same way as Blamey’s interjunction. However, the article explains that since Blamey’s partial logic with interjunction is a logic without tautologies, it does not satisfy some salient conditions of being a logic of atomic transactions. The article introduces a logic of the considered kind, and provides an example of the formal exposition of the case (...) of an atomic transaction. Finally, the article explains the philosophical significance of the introduced logic. (shrink)

Traditionally legal theorists, whenever engaged in controversy, have agreed on one point: legal norms are par excellence rules which impose obligations. The author examines this assumption, which from another perspective (that of constitutional law, for instance) appears less obvious. In fact, constitutional rules are commoniy empowering norms, norms which do not create duties but powers. To this objection many theorists would reply that empowering rules are incomplete and that they are to be understood as parts of duty‐creating rules. A different (...) position from this traditional stance is that defended in Kelsen's later writings, according to which the fundamental type of norm is the empowering norm. The author discusses Kelsen's three theories on the “ideal form” or structure of the legal norm, with special attention to the third of these, the empowerment theory. (shrink)

A method of constructing Hilbert-type axiom systems for standard many-valued propositional logics was offered by Rosser and Turquette. Although this method is considered to be a solution of the problem of axiomatisability of a wide class of many-valued logics, the article demonstrates that it fails to produce adequate axiom systems. The article concerns finitely many-valued propositional logics of Łukasiewicz. It proves that if standard propositional connectives of the Rosser–Turquette axiom systems are definable in terms of the propositional connectives of Łukasiewicz’s (...) logics, and thus, they are normal ones, then every Rosser–Turquette axiom system for a finite-valued Łukasiewicz’s logic is semantically incomplete. (shrink)

The Legal Knowledge Engineering is a new topic of investigationof Artificial Intelligence. This paper discusses some relevant problems relatedto this new area in a summarized way. Within the Normative Law Theory,one question that arises naturally is that of contradiction, like for example:articles conflicting with other articles inside the same code, codes conflictingwith codes, codes conflicting with jurisprudence, and in general, treatmentswith conflicting propositions in Normative Law Theory. This paper suggeststo treat directly inconsistencies in the Legal Knowledge Engineering; thisengineering has as (...) underlying logic a paraconsistent annotated deontic logic.There are three main approximations in Legal Knowledge Engineering basedon: cases, rules and logic. In this paper, we consider the approximationbased on logic. It is considered a paraconsistent annotated deontic logic.Based on this logic, it is established a new proposal that is called Paraconsistent Legal Knowledge Engineering. For this proposal, it it is suggested ameta-interpreter to support the deontic operators as well as inconsistency —entitled on this paper Paralog D that can be used as a base to handle withthe issues discussed. (shrink)

On the basis of a ten-place comparative value relation, artificially reduced to a binary relation, some human value structures are studied and a concept of value kinematics is proposed. A miniature value logic is outlined, making it possible with precision to handle several explicated value notions and to analyze interrelations between them. Finally, the question is discussed whether health can be said to be an absolute and an intrinsic value.