Logical derivation search with assumption traceability

In this paper authors research the problem of traceability of assumptions in logical derivation. The essence of this task is to trace which assumptions from the available knowledge base of assumptions are necessary to derive a certain conclusion. The paper presents a new derivation procedure for propositional logic, which ensures traceability feature. For the derivable conclusion formula derivation procedure also returns the smallest set of assumptions those are enough to get derivation of the conclusion formula. Verification of the procedure were performed using authors implementation.

Value-form and the mystery of money

Value-form is a theory Marx first developed in Capital vol.1 to solve the mystery of money. He seemed convinced that he had finally solved the mystery of money by reducing the money-form to the general value-form. However, his explanation of the transition from the latter to the former with the phrase ‘by social custom’ is not satisfactory. I consider that, as long as a logical derivation of the money-form from the general value-form is unsuccessful, the mystery of money is not yet completely solved. I attempt first to rehabilitate the simple value-form, comparing it with real value expression in price (money-form), emphasizing the distinction between the expression of value and the measure of value, and the asymmetry of the value-form. Thereby, I explain that Marx’s complicated exposition of the value-form stems from his postulate of the labor substance of value in the first chapter of Capital vol.1, which can be proved and developed later in the production process of capital. Rehabilitation of the value-form can expose a fundamental difference between the general value-form and the money-form, and provide a logical derivation of the money-form. To achieve this aim, it is necessary to reformulate the logical structure of the theory of commodity based on the concept ‘the world of commodities’, which comes to appear more frequently as Marx’s theory of value-form advances.

Discovery, logic of

Bacon, Descartes, Newton and other makers of the Scientific Revolution claimed to have found and even used powerful logics or methods of discovery, step-by-step procedures for systematically generating new truths in mathematics and the natural sciences. Method of discovery was also the prime method of justification: generation by correct method was something akin to logical derivation and thus the strongest justification a claim could have. The ’logic’ of these methods was deductive, inductive or both. By the mid-nineteenth century, logic of discovery was yielding to the more flexible and theory-tolerant method of hypothesis as the ’official’ method of science. In the twentieth century, Karl Popper and most logical positivists completed the methodological reversal from generativism to consequentialism by setting their hypothetico-deductive method against logic of discovery. What is epistemologically important, they said, is not how new claims are generated but how they fare in empirical tests of their predictive consequences. They demoted discovery to the status of historical anecdote and psychological process. Since the late 1950s, however, there has been a revival of interest in methodology of discovery on two fronts – logical and historical. An earlier explosion of work in symbolic logic had led to automata theory, computers, and then artificial intelligence. Meanwhile, a maturing history of science was furnishing information on science as a process, on how historical actors and communities actually discovered or constructed their claims and practices. Now, in the 1980s and 1990s, liberal epistemologists once again admit discovery as a legitimate topic for philosophy of science. Yet attempts to both naturalize and to socialize inquiry pose new challenges to the possibility of logics of discovery. Its strong associations with ’the’ method of science makes logic of discovery a target of postmodernist attack, but a more flexible construal is defensible.

M-Polynomials and Degree-Based Topological Indices of Bismuth Tri-Iodide

The topological index is a numerical quantity based on the characteristics of various invariants or molecular graph. For ease of discussion, these indices are classified according to their logical derivation from topological invariants rather than their temporal development. Degree based topological indices depends upon the degree of vertices. This paper computes degree based topological indices of Bismuth Tri-Iodide chains and sheets with the help of M-polynomial.

On Computational Aspects of Bismuth Tri-Iodide

The topological index is a numerical quantity based on the characteristics of various invariants or molecular graph. For ease of discussion, these indices are classified according to their logical derivation from topological invariants rather than their temporal development. Degree based topological indices depends upon the degree of vertices. This paper computes Zagreb polynomials and redefined first, second and third Zagrebindices of Bismuth Tri-Iodide chains and sheets.

Formal polynomials, heuristics and proofs in logic

This note surveys some previous results on the role of formal polynomials as a representation method for logical derivation in classical and non-classical logics, emphasizing many-valued logics, paraconsistent logics and modal logics. It also discusses the potentialities of formal polynomials as heuristic devices in logic and for expressing certain meta-logical properties, as well as pointing to some promising generalizations towards algebraic geometry.

Some logical and syntactical observations concerning the first-order dependent type system λP

We look at two different ways of interpreting logic in the dependent type system λP. The first is by a direct formulas-as-types interpretation à la Howard where the logical derivation rules are mapped to derivation rules in the type system. The second is by viewing λP as a Logical Framework, following Harper et al. (1987) and Harper et al. (1993). The type system is then used as the meta-language in which various logics can be coded.We give a (brief) overview of known (syntactical) results about λP. Then we discuss two issues in some more detail. The first is the completeness of the formulas-as-types embedding of minimal first-order predicate logic into λP. This is a remarkably complicated issue, a first proof of which appeared in Geuvers (1993), following ideas in Barendsen and Geuvers (1989) and Swaen (1989). The second issue is the minimality of λP as a logical framework. We will show that some of the rules are actually superfluous (even though they contribute nicely to the generality of the presentation of λP).At the same time we will attempt to provide a gentle introduction to λP and its various aspects and we will try to use little inside knowledge.