Deduction Rules Research Articles

Fuzzy logic, deductive rules of inference and linguistic reasoning on knowledge base

In this paper we introduce a notion of knowledge base consisting of statements with truth degree in which every statement may have several truth degrees. A set of rules of inference handling this kind of statements, a deductive reasoning method based on these rules will be considered. The consistency of the knowledge base will be also investigated.

The Debt-Equity Distinction in Corporate Taxation: Does it Work, Does it Matter?

Deductibility of interest under corporate income taxation creates a clear and strong incentive to finance corporate investments out of debt rather than equity. For MNEs, there is also a clear and strong incentive to create internal debts as a tax planning tool. National tax legislation in Western Europe seems to be based increasingly on a notion that deduction of interest is somehow “suspect” – that it means “avoiding tax”. In that same policy context, the issue of over-leverage is also addressed as a problem: by trying to avoid the taxman, the corporate sector seems to run straight into the arms of the financial industry. It will be argued in this contribution that, as far as empirical observation is available, both over-leverage and MNE tax planning through internal borrowing seem to be problems of modest size. In the light of the frequent changes in interest deduction rules in many national corporate tax systems, this may come as a surprise. The case for broad system reforms, such as an ACE or a CBIT, is theoretically strong, esp. if combined into a tax that exempts all normal return (e.g., 5%) while taxing all rents whatever the source of finance. But the practical and political attractiveness of such broad approaches is limited. A brief discussion of tax policy developments in the Netherlands is used to illustrate that point. The outcome may be that the best we can do in this area of tax legislation is - as Winston Churchill used to say - keep buggering on.

Financial Transaction Tax: An Eleven-Point Analysis of Transaction Taxes Across Member States

This article analyses the European Commission's Proposal for Financial Transaction Tax with transaction taxes currently implemented in Member States of the European Union. The features identified for this purpose include transactions liable to tax, recognition of legal title, the tax base, jurisdictional rules, provisions for groups, exemptions, deduction rules and timing considerations. This analysis highlights that the Proposal, in principle, varies little from existing transaction taxes; tax rates are generally low and an extraterritorial effect is found in a number of Member States. The Proposal is however broader in scope and contains limited exemptions. The commonalities found in transaction taxes could help to forge a common framework for future reform of the Proposal whilst differences shed light on problems that may be encountered with respect to implementation. Greater support and guidance will be required.

Why Intuitionistic Relevant Logic Cannot Be a Core Logic

At the end of the 1980s, Tennant invented a logical system that he called “intuitionistic relevant logic” (IR, for short). Now he calls this same system “Core logic.” In Section 1, by reference to the rules of natural deduction for IR, I explain why IR is a relevant logic in a subtle way. Sections 2, 3, and 4 give three reasons to assert that IR cannot be a core logic.

Tax Reform Consequent upon an Embedded Single-Rate Vat Just Might Prevent Injustice While Revivifying a Geriatric Uncle Sam

<p class="1"><span lang="EN-US">Economists and legislators have proposed many theories and plans for overhauling the corporate tax system (and the U.S. tax system as a whole); however, this Article argues that any viable proposal should begin with the enactment of a value added tax (VAT).</span></p><p class="1"><span lang="EN-US">As a result of the IRC's unworkably complex corporate section, the United States economy has been hindered by high compliance costs and the loss of business overseas. Overall, a substantial federal VAT is the best option in terms of compliance and administration costs as well as reducing opportunities for federal tax evasion. But merely placing a VAT on top of the existing system would merely send us in reverse by further increasing the variable and substantial fixed costs of administration and compliance. A mere changing of the marginal rates or deduction rules would be insufficient to deal with the systematic problem caused by the yawning federal deficit and the arcane IRC. A VAT rate set too low would impose substantial costs per dollar of additional revenue. Thus, Congress should enact either a federal VAT (15%) capable of significantly reducing the federal deficit or none at all.</span></p>

A logic of graded attributes

We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ? B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects (rows) have attributes (columns); second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees form a scale equipped with operations representing many-valued logical connectives. If 0 and 1 are the only degrees, the algebra of degrees becomes the two-element Boolean algebra and the two interpretations become well-known dependencies in Boolean data and functional dependencies of relational databases. In a setting with general scales, we obtain a new kind of dependencies with naturally arising degrees of validity, degrees of entailment, and related logical concepts. The deduction rules of the proposed logic are inspired by Armstrong rules and make it possible to infer dependencies to degrees--the degrees of provability. We provide a soundness and completeness theorem for such a setting asserting that degrees of entailment coincide with degrees of provability, prove the independence of deduction rules, and present further observations.

Automatic C Program Verification Based on Mixed Axiomatic Semantics

The development of the C-light project resulted in the application of new formalisms and implementation techniques which facilitate the verification process. The mixed axiomatic semantics proposes a choice between simplified and full-strength deduction rules depending on program objects and their properties. The LLVM infrastructure helps greatly in writing the C-light program analyzer and translator. The semantical labeling technique, proposed earlier, can now be safely kept in verification conditions during their proof. Two programs from the well-known verification benchmarks illustrate the applicability of the system.

The taxation of foreign profits: A unified view

This paper synthesizes and extends the literature on the taxation of foreign source income in a framework that covers both greenfield and acquisition investment, and a general constraint linking investment at home and abroad for the multinational by introducing a cost of adjustment for the mobile factor. Unless the cost of adjustment is zero, the domestic tax on foreign-source income should always be set to ensure the optimal allocation of the mobile factor between domestic and foreign assets and should follow the classical rules in the literature; national optimality requires the deduction rule, and global optimality requires the credit rule. Only in the zero-cost case does exemption become optimal. Allowances can be set so as to ensure that domestic and foreign asset purchases are undistorted by the tax system: this requires a cash-flow tax on domestic investment in the greenfield case, and a cross-border cash flow tax on foreign investment in both cases. These basic results extend to various extensions of the model, notably: (i) when a profit-shifting motive is present; and (ii) to some extent, when a corporate income tax is in place. The introduction of tax administration costs into the model can explain the empirical trend towards the use of the exemption regime.

The Taxation of Foreign Profits: A Unified View

This paper synthesizes and extends the literature on the taxation of foreign source income in a framework that covers both greenfield and acquisition investment, and a general constraint linking investment at home and abroad for the multinational by introducing a cost of adjustment for the mobile factor. Unless the cost of adjustment is zero, the domestic tax on foreign-source income should always be set to ensure the optimal allocation of the mobile factor between domestic and foreign assets and should follow the classical rules in the literature; national optimality requires the deduction rule, and global optimality requires the credit rule. Only in the zero-cost case does exemption become optimal. Allowances can be set so as to ensure that domestic and foreign asset purchases are undistorted by the tax system: this requires a cash-flow tax on domestic investment in the greenfield case, and a cross-border cash flow tax on foreign investment in both cases. These basic results extend to various extensions of the model, notably (i) when a profit-shifting motive is present; (ii) to some extent, when a corporate income tax is in place. The introduction of tax administration costs into the model can explain the empirical trend towards use of the exemption regime.

QPEL: Quantum Program and Effect Language

We present the syntax and rules of deduction of QPEL (Quantum Program and Effect Language), a language for describing both quantum programs, and properties of quantum programs - effects on the appropriate Hilbert space. We show how semantics may be given in terms of state-and-effect triangles, a categorical setting that allows semantics in terms of Hilbert spaces, C*-algebras, and other categories. We prove soundness and completeness results that show the derivable judgements are exactly those provable in all state-and-effect triangles.

A note on axiomatizations of Pavelka-style complete fuzzy logics

Pavelka-style completeness, a property relating degrees of provability and truth, was previously studied mainly in the context of logics with continuous connectives. It is known that in some other logics one can use infinitary deduction rule(s) to retain this form of completeness. The present paper offers a systematic study of this idea for fuzzy logics which expand MTL and are given by a fixed standard algebra. We explore the structure of the class of all ‘reasonable’ expansions of any such logic by rational truth constants and, for several prominent cases, provide axiomatizations of particular expansions enjoying the Pavelka-style completeness.

Combinatorial structure of type dependency

We give an account of the basic combinatorial structure underlying the notion of type dependency. We do so by considering the category of generalised algebraic theories in the sense of Cartmell, and exhibiting it as the category of algebras for a monad on a presheaf category. The objects of the presheaf category encode the basic judgements of a dependent sequent calculus, while the action of the monad encodes the deduction rules; so by giving an explicit description of the monad, we obtain an explicit account of the combinatorics of type dependency. We find that this combinatorics is controlled by a particular kind of decorated ordered tree, familiar from computer science and from innocent game semantics. Furthermore, we find that the monad at issue is of a particularly well-behaved kind: it is local right adjoint in the sense of Street–Weber. In future work, we will use this fact to describe nerves for dependent type theories, and to study the coherence problem for dependent type theory using the tools of two-dimensional monad theory.

Perfect Pavelka Logic

Zadeh's Fuzzy Logic was introduced as a mathematical tool for deduction working with different degrees of truth, instead of the two truth degrees of Classical Logic. The next step taken by Pavelka was to admit assumptions and theorems which are also satisfied only to some truth degree, as well as deduction rules transferring these degrees to the deduced formulas. In the semantics these possibly, but not necessarily, correspond to the degrees of satisfaction of formulas. A significant consequent progress towards this direction was achieved by Hajek's work on Rational Pavelka Logic; it forms formulas with graded truth as couples of a formula and a rational truth value. The success of the Rational Pavelka Logic follows from the properties of the standard MV-algebra, i.e. the real unit interval [0,1] with the Łukasiewicz operations, which was used as its semantical interpretation. The main mathematical result is that the Rational Pavelka Logic is sound and complete in the sense that the syntactical provability degree and the semantical degree of satisfaction coincide. In this paper an alternative to Pavelka's approach is investigated. Instead of the standard MV-algebra, the truth values are taken from a perfect MV-algebra, in particular, Chang's MV-algebra. This is the opposite extreme among MV-algebras, it admits only infinitesimals besides the two classical truth degrees. We argue that such an example also has a motivation in deduction imitating human reasoning. As Chang's MV-algebra is not complete, the provability degree need not exist. Nevertheless, as the main result the following weak completeness theorem is proved: If the provability degree of a formula exists, it coincides with the degree of satisfaction. This result is obtained by adding to Pavelka's original approach a new rule of inference, Hájek's book-keeping axioms and an axiom valid in Chang's MV-algebra. An example that clarifies the differences between Classical Logic, Rational Pavelka Logic and Perfect Pavelka Logic is given, and some new fuzzy rules of inference are introduced.

SELF-LEARNING SCORING MODELS – INTRODUCTION OF AN ON-LINE APPROACH TO RISK ASSESMENT

The problem considered in this article involves the construction of evaluation model, which could subsequently be used in the field of modeling and risk management. The research work is finalized by a construction of a new model on the basis of observa tions of the models used for risk management and knowledge of information theory, machine learning and artificial neural networks. The developed tools are trained on line, using their ability for automatic deduction rules based on data, during model application for evaluation tasks. The model, consequently changes the data analysis stage, limits the scope of the necessary expertise in the area, where the assessment model can be used and, to some extent, the shape of the model becomes independent from the current range of available data. These features increase its ability to generalize and to cope with the data of previously undefined classes, as well as improve its resistance to gaps occurring in the data. Performance of the model presented in this paper is tested and verified on the basis of real-life data, which would resemble a potentially real practical application. Preliminary tests performed within the scope of this work indicate that the developed model can form a starting point for further research as some of the used mechanisms have a fairly high efficiency and flexibility.

Argumentation systems: Medical applications

Decision making in medicine is based on logical constructions in the form of reasonings. The paper considers different argumentation instruments used in the clinical practice: arguments and counter arguments, propositional variables, truth values, non-associative logical links, argued and arguing statements, branching of deduction rules, argumentation trees, multi-level argumentation instruments, and generated hypotheses.

K v. Finland: EU Developments in the Area of Foreign Loss Deduction Rules

This article describes the recent judgment of the Court of Justice of the European Union (the Court) in K. v. Finland. The decision considers a Finnish rule disallowing the deduction of a loss on the sale of property situated in another Member State, when that loss exceeds the amount of foreign income received by the resident taxpayer. The Court has examined the deduction of foreign losses on several occasions in the past. This article is therefore an opportunity to assess whether the Court's recent decision is in line with its earlier case law and to what extent it develops the previously established principles.

A sound and complete R-calculi with respect to contraction and minimal change

AGM postulates are for belief revision (revision by a single belief), and DP postulates are for iterated revision (revision by a finite sequence of beliefs). R-calculus is given for R-configurations Δ|Γ, where Δ is a set of atomic formulas or the negations of atomic formulas, and Γ is a finite set of formulas. We shall give two R-calculi C and M (sets of deduction rules) such that for any finite consistent sets Γ, Δ of formulas in the propositional logic, there is a consistent set Θ ⊆ Γ of formulas such that Δ|Γ ⟹ Δ, Θ is provable and Θ is a contraction of Γ by Δ or a minimal change of Γ by Δ; and prove that C and M are sound and complete with respect to the contraction and the minimal change, respectively.

Pruning irrelevant association rules using knowledge mining

The efficiency of existing association rules mining algorithms afford large number of delivered rules that the user can not exploit them easily. Consequently, thinking about another mining of these generated rules becomes essential task. For this, the present paper explores metarules extraction in order to prune the irrelevant rules. It first focuses on clustering association rules for large datasets. This allows the user better organising and interpreting the rules. To more go down in our mining, different dependencies between rules of the same cluster are extracted using meta-rules algorithm. Then, pruning algorithm uses these dependencies to delete the deductive rules and keep just the representative rules for each cluster. The proposed approach is tested on different experiments including clustering, meta-rules and pruning steps. The result is very promising in terms of the number of returned rules and their quality.

PEMIKIRAN SYAUQI DHAIF DAN UPAYA PEMBAHARUANNYA DI BIDANG PENGAJARAN NAHWU (Telaah Buku Tajdid al-Nahwi Karya Syauqi Dhaif)

Science of Nahwu is recognized as a discipline that is loaded with a variety of rules and theories, as the result of a process of a long journey in the history of Arabic linguistics. Starting from the codification and systemization activities of Arabic vocabulary is quite time consuming, then linguists (al-Lughawiyyûn / linguist) construct and lay the basic principles of the rules of the language. The basic principles of nahwu at first is very simple then evolved into a "science" which is very complicated and cumbersome. Nahwu is no longer just functions as a deductive rule or a grammar, but it also has become one of the instruments to understand the Qur'an itself, which in turn gave rise to many theories nahwu developed by experts nahwu (nuhât / Grammarian). This, of course, more difficult to understand and learn the science of Nahwu itself. For the purposes of education and teaching that is deemed necessary rethinking and renewal (tajdid) in the field of teaching and teaching nahwa materials simplification.

Decision implications: a logical point of view

This paper serves to present the semantical and syntactical aspects of decision implications. In the semantical aspect, we will introduce the notions of “closure” and “unite closure”, representing the closure of condition attributes with respect to decision attributes and the closure with respect to the whole attribute set respectively. In the syntactical aspect, we form two deduction rules, namely Augmentation and Combination, and prove that they are complete with respect to the semantical aspect. Moreover, we describe an approach to obtain a decision context from a given set of decision implications, and show that the decision context obtained can produce the same set of decision implications.