Showing papers on "Paraconsistent logic published in 1978"

Multiple-conclusion logic

Abstract: Multiple-conclusion logic extends formal logic by allowing arguments to have a set of conclusions instead of a single one, the truth lying somewhere among the conclusions if all the premises are true. The extension opens up interesting possibilities based on the symmetry between premises and conclusions, and can also be used to throw fresh light on the conventional logic and its limitations. This is a sustained study of the subject and is certain to stimulate further research. Part I reworks the fundamental ideas of logic to take account of multiple conclusions, and investigates the connections between multiple - and single - conclusion calculi. Part II draws on graph theory to discuss the form and validity of arguments independently of particular logical systems. Part III contrasts the multiple - and the single - conclusion treatment of one and the same subject, using many-valued logic as the example; and Part IV shows how the methods of 'natural deduction' can be matched by direct proofs using multiple conclusions.

First order logic formalization for functional, multivalued and mutual dependencies

Abstract: The purpose of this paper is to show that first order logic is adequate for formalizing functional, multivalued and mutual dependencies in relational data bases. Advantages of using logic instead of tailored formal systems are presented. This paper is decomposed into four sections. The first one presents some notions of logic and theorem proving which are relevant to this study. In the second section, a way to analyze data bases in terms of logic is briefly indicated. The third section deals with the expression of dependency statements as formulas of logic. Lastly section 4 is concerned with some properties of dependency statements which follow directly from the proposed formalization.

The Logic of Interpretation

Abstract: One of the more important and controversial problems in contemporary analytic aesthetics concerns the logic of critical interpretation. There appear to be at least three distinguishable, though closely related, aspects of the problem. The first concerns the logical status of interpretative statements. Do such statements express propositions with some sort of truth value or do they merely express decisions or recommendations? If the former, are these propositions really about the work itself or only about the critic's way of seeing it? Again, if interpretations do express propositions about the work itself, are they in principle determinable as true or false, or only at best as plausible or implausible? Critics typically support their interpretations with reasons. The second aspect of the problem thus concerns the logical role of these reasons. Do they function as real evidence logically supporting an interpretative conclusion, or are they but rhetorical devices to persuade the reader to adopt the critic's point of view? Are they perhaps but further descriptions of the critic's experience of the work, or are they aids for focusing attention on something or for creating a desired perception in the reader? The third aspect, intimately connected with the second, concerns the general form or character of interpretative argument. If these arguments are indeed logical, is their logic typically inductive, deductive, or rather something entirely different? In their attempt to determine the logic of interpretation, analytic philosophers of art have propounded very different views regarding these three aspects of the problem, often without distinguishing between them. It should be stressed that for these philosophers the attempt to determine the logic of interpretation is primarily an analytic or descriptive matter, not a normative or legislative one.1 Their aim is to analyse the logic actually employed in interpretation, not to recommend a logic that should be employed; they claim to describe what qualified critics actually do in interpreting, not to prescribe what they should do. Yet when we survey the results of their analyses, we find a perplexingly wide divergence of views. Aestheticians hotly debate which of these analyses of interpretative logic is the correct one, but seem to be getting no closer to the solution of this question. 1Some analytic aestheticians do, however, make critical recommendations, e.g., Beardsley, whose "intentional fallacy" is a case of legislating against authorial intention as a goal or standard of criticism. See M. C. Beardsley, The Possibility of Criticism (Detroit, 1973).

Only If Quanta Had Logic

Abstract: Putnam and others have argued that an examination of structures arising in quantum mechanics can lead to a non-classical propositional logic, quantum logic. In this paper it is argued that the procedure by which quantum logic is said to be discovered, a process called reading off, is fundamentally flawed. A parody fable shows that reading off leads to absurd consequences. The fable also leads one to cast doubt on the following claims central to the quantum logic program: (i) logic can be reformed locally; (ii) classical logic is read off classical physics; and (iii) reading off is a justifiable process because quantum logic resolves quantum paradoxes.

Concluding Remarks: Classical Logic and Quantum Logic

Abstract: The considerations of Chapters 3–5 have led to the result that the most general propositional logic which is equally applicable to propositions about classical and quantum mechanical systems is given by the calculus Q eff of effective quantum logic. In addition, in Chapter 6 we have shown that, by a weak assumption concerning the confirmation of commensurability propositions, this calculus can be extended to the calculus Q of full quantum logic. Hence, one arrives at the conclusion that the ‘true’ logic is given by the calculus of full quantum logic, whereas ordinary effective logic and classical propositional logic are formal systems, the validity of which is restricted to the special case of unrestrictedly available (commensurable) propositions. In particular, propositions about physical systems have this property to the extent that the system in question can be considered as a classical one. Consequently, from this point of view classical propositional logic turns out to be an idealisation, which has only approximate validity and, thus, no fundamental meaning.