Deduction Rules Research Articles

Maani Letters and Their Influence in Facilitating Islamic Jurisprudence Analytical Study of Waw Athaf Letters in Ahkam Verses/ حروف المعاني وأثرها في تيسير الحكم الفقهي واو العطف نموذجا، دراسة تحليلية في بعض آيات الأحكام

The letters of meanings are a linguistic topic that the fundamentalists borrowed in the field of fundamentals, and they may have added appreciable additions to it to achieve the goal of lending it to science. This is because of its importance in deducing legal rulings. This appears in the way fundamentalists deal with it in their books, ancient and modern. But there is another essential feature, which is that the conjunctions, or the letters of meanings, by contemplating the places they appear in the verses of rulings - and the hadiths of rulings by extension - we found that they have an essential effect in deducing rulings on the one hand, and in facilitating jurisprudential rulings on the other hand. The fundamentalists have worked hard to explain the meanings of the letters of meaning, including the conjunctions, and to explain the impact of this on deducing legal rulings. They have made great efforts in doing so. They based many of the deduction rules on rules in the Arabic language. This research focuses on the letter waw, as it is one of the conjunctions of the meaning letters, and shows its effect in deriving legal rulings while presenting its role in facilitating jurisprudential rulings, which is consistent with the intention of the law and its will in basing rulings on facilitation.

A Review of Non-Isolated High-Gain Y-Source Converters Topologies

Due to the low voltage and high randomness of renewable energy, high-performance grid-connected converters are needed. With the advantages of a high boost ratio, flexible design, and simple control, the Y-Source Converter (YSC) is widely concerned. However, there are a few drawbacks to the traditional Y-source converter, including significant switching stress, voltage voltage overshoot, and discontinuous current. To solve the problems above, a series of improved topologies are proposed. Moreover, the voltage gain, current ripple, and soft switching characteristics have also been optimized. So far, the existing literature lacks the collation and comparison of different topologies of Y-source, as well as the analysis of its evolution process. Therefore, this paper provides a comprehensive overview of Y-source converters’ topologies. According to their features and applications, different topologies are classified and described, leading to guidance for the selection of YSCs under different scenarios. Meanwhile, the working principle, evolution process, and vital issues are analyzed. By revealing their deductive rules, valuable suggestions are provided for the future development of YSCs.

Deductive Reasoning Based on the Valid Aristotelian Syllogism AEE-2

This paper firstly formalizes Aristotelian syllogisms based on the tripartite structure of categorical propositions, and then uses the truth definitions of categorical propositions to prove the validity of the Aristotelian syllogism AEE-2. Then, the remaining 23 valid syllogisms are derived from the syllogism AEE-2 with the help of relevant facts, inner and outer negation definitions of quantifiers, and deductive rules. In other words, this paper reveals the reducible relationship between/among these 24 syllogisms and establishes a succinct formal reason system for Aristotelian syllogistic. The deductive reasoning not only ensures consistency in its results, but also provides a concise mathematical paradigm for other types of syllogisms.

The Place of Reduction in Aristotle's Prior Analytics

Studies of Aristotle’s syllogistic system, since Corcoran’s deductionist interpretation supplanted Łukasiewicz’ axiomaticist interpretation, misrepresent Aristotle’s logic in two important respects. Following Corcoran, they take indirect deduction to occur only once in a deduction discourse; they then obviate the system having a reductio rule. Second, they represent reduction as a deductive process for deriving ‘imperfect’ syllogisms from ‘perfect’ syllogisms to impose an axiomatic interpretation on the logic. Denying that Aristotle's logic admits of a reductio rule results from this misrepresentation of reduction. This discussion shows that the defects imputed to Aristotle's logic, and systems devised to resolve them, result from misunderstanding reduction, which itself results from misapprehending Prior Analytics expressly to identify in a metadiscourse deduction rules and not deductions per se.

Electrophysiological connectivity of logical deduction: Early cortical MEG study

Complex human reasoning involves minimal abilities to extract conclusions implied in the available information. These abilities are considered “deductive” because they exemplify certain abstract relations among propositions or probabilities called deductive arguments. However, the electrophysiological dynamics which supports such complex cognitive processes has not been addressed yet. In this work we consider typically deductive logico-probabilistically valid inferences and aim to verify or refute their electrophysiological functional connectivity differences from invalid inferences with the same content (same relational variables, same stimuli, same relevant and salient features). We recorded the brain electrophysiological activity of 20 participants (age = 20.35 ± 3.23) by means of an MEG system during two consecutive reasoning tasks: a search task (invalid condition) without any specific deductive rules to follow, and a logically valid deductive task (valid condition) with explicit deductive rules as instructions. We calculated the functional connectivity (FC) for each condition and conducted a seed-based analysis in a set of cortical regions of interest. Finally, we used a cluster-based permutation test to compare the differences between logically valid and invalid conditions in terms of FC. As a first novel result we found higher FC for valid condition in beta band between regions of interest and left prefrontal, temporal, parietal, and cingulate structures. FC analysis allows a second novel result which is the definition of a propositional network with operculo-cingular, parietal and medial nodes, specifically including disputed medial deductive “core” areas. The experiment discloses measurable cortical processes which do not depend on content but on truth-functional propositional operators. These experimental novelties may contribute to understand the cortical bases of deductive processes.

A new connective in natural deduction, and its application to quantum computing

We investigate an unsuspected connection between logical connectives with non-harmonious deduction rules, such as Prior's tonk, and quantum computing. We argue that these connectives model the information-erasure, the non-reversibility, and the non-determinism that occur, among other places, in quantum measurement. We introduce an intuitionistic propositional logic with a non-harmonious logical connective sup and two interstitial rules, and show that the proof language of this logic forms the core of a quantum programming language.

An Algebra of Alignment for Relational Verification

Relational verification encompasses information flow security, regression verification, translation validation for compilers, and more. Effective alignment of the programs and computations to be related facilitates use of simpler relational invariants and relational procedure specs, which in turn enables automation and modular reasoning. Alignment has been explored in terms of trace pairs, deductive rules of relational Hoare logics (RHL), and several forms of product automata. This article shows how a simple extension of Kleene Algebra with Tests (KAT), called BiKAT, subsumes prior formulations, including alignment witnesses for forall-exists properties, which brings to light new RHL-style rules for such properties. Alignments can be discovered algorithmically or devised manually but, in either case, their adequacy with respect to the original programs must be proved; an explicit algebra enables constructive proof by equational reasoning. Furthermore our approach inherits algorithmic benefits from existing KAT-based techniques and tools, which are applicable to a range of semantic models.

A finitary outer measure logic

Abstract We extend classical first-order logic with a family of weak probability quantifiers, which we call submeasure quantifiers. Formulas are finitary, but infinitary deduction rules are needed. We consider first-order structures that are equipped with a countable family of submeasures (hence the name of the new quantifiers). We prove that every consistent set of sentences in the resulting logic is satisfiable in some structure as above. Then we restrict the set of formulas by requiring that no submeasure quantifier occurs within the scope of some classical quantifier. By suitably extending the deduction rules, we prove that every consistent set of sentences from the restricted class of formulas is satisfiable in some structure whose submeasures are actually outer measures. To perform the last step, we apply nonstandard techniques à la A. Robinson.

Formal System of Categorical Syllogistic Logic Based on the Syllogism <i>AEE-4</i>

Adopting a different method from the previous scholars, this article deduces the remaining 23 valid syllogisms just taking the syllogism AEE-4 as the basic axiom. The basic idea of this study is as follows: firstly, make full use of the trichotomy structure of categorical propositions to formalize categorical syllogisms. Then, taking advantage of the deductive rules in classical propositional logic and the basic facts in the generalized quantifier theory, we deduce the remaining 23 valid categorical syllogisms by taking just one syllogism (that is, AEE-4) as the basic axiom. This article not only reveals the reducible relations between the syllogism AEE-4 and the other 23 valid syllogisms, but also establishes a concise formal axiomatic system for categorical syllogistic logic. We hope that the results and methods will provide a good mathematical paradigm for studying other kinds of syllogistic logics, and that the project will appeal to specialists in logic, linguistic semantics, computational semantics, cognitive science and artificial intelligence.

Lang-n-Send Extended: Sending Regular Expressions to Monitors

In prior work, Cimini has presented Lang-n-Send, a pi-calculus with language definitions. In this paper, we present an extension of this calculus called Lang-n-Send+m. First, we revise Lang-n-Send to work with transition system specifications rather than its language specifications. This revision allows the use of negative premises in deduction rules. Next, we extend Lang-n-Send with monitors and with the ability of sending and receiving regular expressions, which then can be used in the context of larger regular expressions to monitor the execution of programs. We present a reduction semantics for Lang-n-Send+m, and we offer examples that demonstrate the scenarios that our calculus captures.

Pareto-improving reforms of tax deductions

We analyze Pareto-efficient tax deduction rules for work-related expenses. Pareto efficiency dictates a strict rule for marginal deductions along the income distribution. An immediate implication is a recipe for designing Pareto-improving reforms. We apply our theory and simulate a Pareto-improving reform that introduces deductions for non-care household services (housekeeping, gardening, laundry) in the United States. The reform combines marginal deduction rates for household services between 55% and 85% with a slight increase in marginal tax rates.

Domain object hierarchies inducing multi-level models

Conceptual modeling of domain object hierarchies, such as product hierarchies or organization hierarchies, is difficult due to the intricate nature of nonphysical domain objects organized in such hierarchies. Modeling domain object hierarchies as part-whole hierarchies covers their hierarchical structure, yet to capture their meaning, part-whole hierarchies have to be combined with specialization and multi-level instantiation. To this end we introduce the deep domain object (DDO) multi-level modeling pattern and approach. With the DDO approach, subclasses and metaclasses are induced by and integrated with the part-whole hierarchy. The approach is aligned with the multi-level theory (MLT) and formalized by a metamodel and a set of deductive rules implemented in F-Logic. The proof-of-concept prototype is used for automated application of the pattern and for querying induced multi-level models.

Introduction: Investigating Explicit L2 Grammar Instruction Through Multiple Theoretical and Methodological Lenses

AbstractThe articles in this special issue apply a variety of theoretical and methodological perspectives to quantitative and qualitative data gathered in eight third‐year, intermediate second‐language (L2) Spanish classes at three U.S. high schools (N = 195). The goal of this research was to document grammatical development through two forms of explicit instruction on the pronoun se: one involving deductive rule presentations, and the other involving an inductive “co‐construction” of grammatical rules with learners (Adair‐Hauck et al., 2005). After reviewing cognitive and social approaches to explicit instruction, I present the context and procedures for data gathering, followed by an overview of the main findings in each article. While quantitative results suggest a somewhat stronger performance for the deductive group, qualitative evidence suggests a more challenging task for teachers implementing co‐construction. I conclude emphasizing the value of high‐quality explicit instruction to L2 development and the importance of teachers in making that happen.

Modelling the impacts of crowds on occupants in the built environment—A static, rule-based approach to human perception and movement

A building occupant’s experiences are not passive responses to environmental stimuli, but are the results of multifaceted, prolonged interactions between people and space. We present a framework and prototype software tool for logically reasoning about occupant perception and behaviour in the context of dynamic aspects of buildings in operation, based on qualitative deductive rules. In particular, we focus on the co-presence of different user groups and the resulting impact on perceptual and functional affordances of spatial layouts by utilising the concept of spatial artefacts. As a first proof of concept of our approach, we have implemented a prototype crowd analysis software tool in our new system ASP4BIM, developed specifically to support architectural design reasoning in the context of public-facing buildings with complex signage systems and diverse intended user groups. We evaluate our prototype on the Urban Sciences Building at Newcastle University, a large, state-of-the-art living laboratory and multipurpose academic building. Our findings are that the ASP4BIM-based prototype supports a range of novel query services for formally analysing the impacts of crowds on pedestrians that are logically derived through the use of qualitative deductive rules, that complements other powerful crowd analysis approaches such as agent-based simulation.

Modal Logics and Group Polarization

Abstract This paper proposes different ways of modally defining properties related to the concept of balance in signed social networks where relations can be either positive or negative. The motivation is to be able to formally reason about the social phenomenon of group polarization based on balance theory. The starting point is a recently developed basic modal logic that axiomatizes the class of social networks that are balanced up to a certain degree. This property is not modally definable but can be captured using a deduction rule. In this work, we examine different possibilities for extending this basic language to define frame properties such as balance and related properties such as non-overlapping positive and negative relations and collective connectedness as axioms. Furthermore, we define the property of full balance rather than balanced-up-to-a-degree. We look into the complexity of the model checking problem and show a non-compactness result of the extended language. Along the way, we provide axioms for weak balance. We also look at a full hybrid extension and reason about network changes with dynamic modalities. Then, to explore the measures of how far a network is from polarization, we consider variations of measures in relation to balance.

An Authoring Tool to Derive Valid Interactive Scenarios

In recent years, many tools have been proposed to design interactive scenarios. The aim of these tools is to provide users with a framework in order to write a story with many branches which will be unfolded by an artificial intelligence application. However, the consistency and quality of the generated narratives are not guaranteed (deadlocks, flaws, etc.). Previous work has defined the properties of a valid interactive scenario and proposed an approach as well as a tool based on a formal model, Linear Logic, to validate these properties. Nevertheless, the application of this tool requires many special skills and so is not really suitable for normal users. In this paper, we present an authoring tool which allows modeling interactive scenarios and analysing them at the structural level using the deduction rules in Linear Logic. Thanks to our tool, normal users are able to create and validate interactive scenarios in comparison with a rich set of predefined properties/criteria of quality.

From 2-Sequents and Linear Nested Sequents to Natural Deduction for Normal Modal Logics

We extend to natural deduction the approach of Linear Nested Sequents and of 2-Sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction: only one introduction and one elimination rule per connective, no additional (structural) rule, no explicit reference to the accessibility relation of the intended Kripke models. We give systems for the normal modal logics from K to S4. For the intuitionistic versions of the systems, we define proof reduction, and prove proof normalization, thus obtaining a syntactical proof of consistency. For logics K and K4 we use existence predicates (à la Scott) for formulating sound deduction rules.

THE COPERNICAN MULTIVERSE OF SETS

AbstractWe develop an untyped framework for the multiverse of set theory.$\mathsf {ZF}$is extended with semantically motivated axioms utilizing the new symbols$\mathsf {Uni}(\mathcal {U})$and$\mathsf {Mod}(\mathcal {U, \sigma })$, expressing that$\mathcal {U}$is a universe and that$\sigma $is true in the universe$\mathcal {U}$, respectively. Here$\sigma $ranges over the augmented language, leading to liar-style phenomena that are analyzed. The framework is both compatible with a broad range of multiverse conceptions and suggests its own philosophically and semantically motivated multiverse principles. In particular, the framework is closely linked with a deductive rule of Necessitation expressing that the multiverse theory can only prove statements that it also proves to hold in all universes. We argue that this may be philosophically thought of as aCopernican principlethat the background theory does not hold a privileged position over the theories of its internal universes. Our main mathematical result is a lemma encapsulating a technique for locally interpreting a wide variety of extensions of our basic framework in more familiar theories. We apply this to show, for a range of such semantically motivated extensions, that their consistency strength is at most slightly above that of the base theory$\mathsf {ZF}$, and thus not seriously limiting to the diversity of the set-theoretic multiverse. We end with case studies applying the framework to two multiverse conceptions of set theory: arithmetic absoluteness and Joel D. Hamkins’ multiverse theory.

Analysis in Prior Analytics I.45

I reconstruct Aristotle’s analytical procedure in Prior Analytics I.45 and its metalogical implications. Aristotle’s analysis unfolds three groups of syllogisms: symmetrically analysable, asymmetrically analysable, and non-analysable syllogisms. From the first and the third group could be extracted 27 combinations of the two mutually non-derivable deductive rules. Aristotle’s reduced deductive system in APr. I.7 with the two moods in the first figure (traditionally called Barbara and Celarent) follows this pattern. I demonstrate that the deductive system with Barbara and Celarent is just one of 27 possible complete deductive systems with the two mutually non-derivable syllogistic rules. On top of that, given the fact that there are two combinations of mutually non-derivable conversion rules, I conclude that Prior Analytics hides in itself 54 complete deductive systems with a minimal number of mutually non-derivable rules. Finally, it is commented what might be the role of analysis; to what extent Aristotle could be aware of possibilities presented here; why he still prefers only one deductive system to many others with the same deductive power.

Simple rules and the Political Economy of Income Taxation: the strengths of a uniform expense rule

The complexity of the U.S. income tax system emerged in part from the differentiated fiscal treatment of specific investments and various sorts of business expenditures that, as Richard Wagner says, creates “a tax code so large that no one can read it and which creates nearly a unique tax liability for each taxpayer.” While tax scholarship documents the costs of complexity, current scholarship lacks a normative legal theory that could inspire an alternative to this practice of targeted credits and deduction rules. This paper builds on Epstein’s general Simple Rules framework to develop a radical simplification of income tax: the operationalization of a uniform expense rule, i.e., the application of a single deduction scheme across all expenses and investments. With regard to the trade-off between targeted rules and this general approach, this paper investigates the nature of a uniform expense rule and reveals its strengths with respect to political economy. First, a stable and universal expense rule would narrow the scope of politicians’ ability to concentrate benefits on special-interest groups and would limit rent-seeking. The abolition of deviating rules for investments would restrict the scope of tax optimization, meaning that individual and corporate tax liabilities would be more determined by the ability to pay them. The same policy would save companies and government millions of dollars that they currently spend on tax compliance and administration of the tax system, respectively. Last, a deduction rule that applies across all businesses and industries would be less price distortive and thus would enhance the quality of the price signal.