Logical Extension Research Articles

‘County lines’: racism, safeguarding and statecraft in Britain

Government policies relating to dealers in ‘county lines’ drugs trafficking cases have been welcomed as a departure from punitive approaches to drugs and ‘gang’ policing, in that those on the bottom rung of the drugs economy of heroin and crack cocaine are no longer treated as criminals but as potential victims and ‘modern slaves’ in need of protection. However, our research suggests not so much a radical break with previous modes of policing as that the term ‘county lines’ emerged as a logical extension of the government’s racist and classist language surrounding ‘gangs’, knife crime and youth violence. Policies implemented in the name of safeguarding the vulnerable also act as a gateway for criminalisation not just under drugs laws but also modern slavery legislation. The government’s discovery of, and responses to, ‘county lines’ hinge on a moral crisis in the making, which ultimately deepens the state’s pre-emptive and violent criminalisation of the ‘Black criminal other’ at a time of deep political crisis.

Influence of ring gear flexibility on the fatigue reliability of planetary gear systems in heavy helicopters

Flexibility of ring gear rims significantly affects the mechanical properties of planetary transmissions at both levels of gear tooth meshing and system power sharing, and is one of the important design factors determining the service reliability of large aviation planetary systems. Therefore, to analyze the mechanism by which the flexibility of ring gear rims affects the fatigue reliability of planetary systems, in the framework of the stress-strength interference theory, a reliability assessment model for the planetary system is constructed based on a calculation logic extension for the full probability formula. Starting from balancing evaluation accuracy and evaluation cost, a hybrid finite element method and a gear tooth lifetime transformation test are employed to provide load and strength input variables for the reliability model respectively. Finally, a mapping relationship from ring gear rim flexibility to planetary system fatigue reliability is established. For the specific design scheme of planetary systems, a lower limit of the ring gear rim thickness can be determined according to the requirements of reliability indexes, so that the balance between reliability and lightweight can be achieved to some extent.

Residuated Basic Logic

Residuated basic logic (RBL) is the logic of residuated basic algebras, which constitutes a conservative extension of basic propositional logic (BPL). The basic implication is a residual of a non-associative binary operator in RBL. The conservativity is shown by relational semantics. A Gentzen-style sequent calculus GRBL, which is an extension of the distributive full non-associative Lambek calculus, is established for residuated basic logic. The calculus GRBL admits the mix-elimination, subformula, and disjunction properties. Moreover, the class of all residuated basic algebras has the finite embeddability property. The consequence relation of GRBL is decidable.

Postulate satisfaction for inconsistency measures in monotonic logics and databases

Inconsistency measures for propositional logic have been investigated in great detail for the past 20 years. Many such measures have been proposed. Rationality postulates, conditions about inconsistency measures, were defined to distinguish the measures that satisfy intuitively desirable properties. The satisfaction or violation of various postulates is known for many inconsistency measures. But propositional logic has many limitations and in many applications more complex logics are appropriate. We consider monotonic extensions of propositional logic such as modal, temporal, description, and first-order logic. We focus on a class of inconsistency measures whose computation depends only on the structure of the minimal inconsistent subsets. The definition of these inconsistency measures is the same for these logics as for propositional logic. The situation is similar for the rationality postulates. This paper studies the connection between the satisfaction or violation of the postulates for propositional logic and monotonic extensions of propositional logic. We show that the results are the same for the most prominent postulates. Additionally, we consider the same question for databases. We show that although the setting is substantially different from these logics, in general the results are the same.

Metric dynamic equilibrium logic

In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behaviour of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. In many applications, however, timing constraints are important like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time Dynamic Equilibrium Logic, in which dynamic operators are constrained by intervals over integers. The resulting Metric Dynamic Equilibrium Logic provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. As such, it constitutes the most general among a whole spectrum of temporal extensions of Equilibrium Logic. In detail, we show that it encompasses Temporal, Dynamic, Metric and regular Equilibrium Logic, as well as its classic counterparts once the law of the excluded middle is added.

Fuzzy correlational analysis for dynamic consolidation of virtual machines in cloud computing environment

This theoretical research in fuzzy correlation analysis integrates data uncertainty analysis by measuring the strength of the linear relationship restricted to two fuzzy sets. As the relevant contribution to this research area, this paper presents the axiomatic definition of the n-dimensional generalized fuzzy correlation coefficient (nGCC), assigning to n input fuzzy sets an output value in the interval [−1,1]. Thus, the properties of general overlap functions and fuzzy negations are studied, discussing binary non-normed restricted dissimilarity functions, and the n-dimensional non-normed conjunctive functions. This study provides new methods for the n-dimensional generalized fuzzy correlation coefficient analysis, regarding their applications in solving multi-criteria and decision-making problems founded on fuzzy logic extensions. The n-dimensional non-normed conjunctive aggregation functions are also introduced, as range domain extensions from [0,1] to [−1.1], covering the interpretation of negative to positive variable associations. The proposal correlation analysis promotes a better evaluation and data selection even when more than one algorithm is applied to evaluate the reduction methods in the defuzzification process based on Interval-valued Fuzzy Logic. We also investigate the relevance to determine a reliable result from the fuzzy inference system based on the nGCC methodology. This correlation methodology applied to the Interval Fuzzy Load Balancing for Cloud Computing (Int-FLBCC) model contributes as a flexible approach for virtual machines dynamic consolidation enabling improvements in resource usage and power efficiency, improving the computational system’s energy efficiency. So, the nGCC methodology extends the Int-FLBCC model by adding other degrees of reliability to the results obtained with diverse evaluations through n-dimensional generalized fuzzy correlation coefficient expressions, exploring average aggregations as arithmetic and exponential means and the median operator.

The green economy as plantation ecology: When dehumanization and ecological simplification go 'green

The green economy is proposed as a solution to address growing and potentially irreversible ecological crises. But what happens when environmental solutions are premised on the same logics of brutal simplification and dehumanization that sustain and reinforce systems of oppression and ecological breakdown? In this article, we describe the transformation of the biophysical landscape of the planet into replicable blueprints of the plantation plot. The plantation as a colonial-era organizational template is an ongoing ecological process premised on disciplining bodies and landscapes into efficient, predictable, calculable, and controllable plots to optimize commodity production and is dependent on racialized and gendered processes of dehumanization. The visible cultural, physical, aesthetic, and political singularity of the plot, under the guise of objectivity and neutrality, permits a tangible depiction of the way ecological breakdown takes place. We interrogate the notion of "greening" as a strategy to combat the unintended impacts of colonial plantation ecology, arguing that such tactics further reinforce the template of plantation ecology rather than dismantle it. We first conceptualize the historical plantation and its biophysical, cognitive, and corporeal organizational principles. We then offer examples of "greening" as new, more inclusive (but equally detrimental) forms of plantation logics, and crucially identify how these extensions of plantation logic get co-opted by resistance agents, from social movements to disease and pestilence. We consider sustainability certifications of palm oil through the Roundtable on Sustainable Palm Oil (RSPO) in Colombia and compensatory afforestation programs designed to offset forest destruction through monoculture plantations in India. We conclude by highlighting how abolition ecologies can serve as an antidote to plantation logic and highlight necessary relationships of self-reflexivity, repair and collective solidarity required to disinvest in plantation ecology.

Finite Tree-Countermodels via Refutation Systems in Extensions of Positive Logic with Strong Negation

A sufficient condition for an extension of positive logic with strong negation to be characterized by a class of finite trees is given.

Dual counterpart intuitionistic logic

Abstract We introduce dual counterpart intuitionistic logic (or DCInt): a constructive logic that is a conservative extension of intuitionistic logic, a sublogic of bi-intuitionistic logic, has the logical duality property of classical logic, and also retains the modal character of its interpretation of the connective dual to intuitionistic implication. We define its Kripke semantics along with the corresponding notion of a bisimulation, and then prove that it has both the disjunction property and (its dual) the constructible falsity property. Also, for any class $ {\mathcal{C}}$ of Kripke frames from our semantics, we identify a condition such that $ {\mathcal{C}}$ will have the disjunction property if it satisfies the condition. This provides a method for generating extensions of DCInt that retain the disjunction property.

On algebraic array theories

Automatic verification of programs manipulating arrays relies on specialised decision procedures. A methodology to classify the theories handled by these procedures is introduced. It is based on decomposition theorems in the style of Feferman and Vaught. The method is applied to obtain an extension of combinatory array logic that is closed under propositional operations and Hoare triples. A classification according to expressiveness of six different fragments studied in the literature is given.

Constitutionalism with Adjectives: Conceptual Innovation in the Comparative Study of Law

The latter half of the twentieth century and the early twenty-first century witnessed a global wave of constitution writing. Scholarly examination of these new charters found that most embodied liberalism and democracy. Additional study, however, found that textual convergence among these “higher law constitutions” belied important heterogeneity in constitutionalism—that is, in the principles underlying these charters and associated attitudes and behaviors. Scholars adopted several conceptual strategies to accommodate this variation, including attaching adjectives to constitutionalism (for example, “globalizing constitutionalism” and “abusive constitutionalism”). This article analyzes this conceptual innovation, drawing on an original dataset of all mentions of the word “constitutionalism” paired with a qualifying adjective found in the title/abstract of articles or in the title/first substantive page of books/dissertations, written in English, published between 1945 and 2019 and referenced on the Internet. We identified 1,621 “adjective-constitutionalism combinations,” including 564 unique combinations, suggesting both extraordinary empirical variation and little coordination among scholars with regard to conceptualization. Moreover, scholars’ conceptualizations of constitutionalism rarely reference equality, justice, or state responsibility for pursuing those ideals, despite these values being logical extensions of higher law constitutions’ core precepts; indeed, some conceptualizations even reflected illiberal or rights-limiting principles of governance. These findings raise the specter of a disconnect between constitutions and constitutionalism that we hope future studies will examine.

Apostolicity II: How does divine apostolicity affect God’s interaction with the world and humanity?

Investigating the research question of how divine apostolicity affects God’s interaction with the world and humanity, predicates apostolicity as being a divine attribute. The logical extension therefore necessitates consideration of the apostolic attribute as an ontological, Trinitarian and operational characteristic demonstrated in the divine-human inter-relationship. Knowledge was drawn from relevant and authoritative sources: Ancient Near Eastern, Israelite, biblical, Hellenistic, reformation and contemporary theological and scientific. They were examined to accurately articulate diverse academic views, to provide critical appraisal of historical, theological and scientific investigation and theoretical frameworks, axiomatic for current and future research. The research method was of necessity an ontological consideration of the nature of God as a transcendent-immanent and relational reality. Epistemological analysis examines the multiple and developing theories of causation, of divine providence determinist or necessitarian, indeterminist or contingent, or an open participatory view of natural order. Philosophical, theological and scientific paradigms expose the founding theoretical principles confronting positivist-determinist and post-positivist-contingent views, thereafter enabling the proposition of an apostolic paradigm. (Cohen et al., 2018: 3, 5-6, 10, 14, 16, 18, 28, 34). The apostolic paradigm articulates a dynamic relationship to the world and humanity with particular attention to New Testament incarnational Christological and pneumatological parameters that postulate a paradigm change and subsequent rereading of the worldview through apostolic dynamic phases. Herein lies the contribution to the existing body of knowledge and contemporary biblical worldview developments in this field.

Rydberg sensors and machine learning assisted design discovery

Recent developments in Machine Learning (ML) models that purport to automate material discovery are explored, with a treatment of the logical extension of this work that we have defined as “Design Discovery”. If we use the Rydberg sensor as a representative target for modeling with advanced ML tools and algorithms, the definition of a sufficient feature set to establish an ML model requires the quantum mechanical description of electrical and magnetic interactions that leverage Stark effect observations and Rydberg states of the targeted atom, as well as other forces internal and external to the atomic structure. This provides a feature rich environment from the standpoint of predictive design using Machine Learning models. The paper concludes with a theoretical treatment of a Rydberg sensor and its potential sensitivity to measurement of extremely small electromagnetic phenomena, with an initial consideration of potential variations of existing experiments that can be “discovered” from an appropriately defined ML design discovery model.

Enhancing long-term smoking abstinence among individuals with a history of cervical intraepithelial neoplasia or cervical cancer (Project ACCESS): protocol for a randomized clinical trial

BackgroundThe prevalence of smoking among cervical cancer survivors is high and evidence-based smoking cessation interventions are critically needed. This paper describes the study design, methods, and data analysis plans for a randomized clinical trial (RCT) designed to evaluate the efficacy of a novel, personally tailored SMS-delivered text-based digital treatment adjuvant designed to enhance the long-term efficacy of a “Motivation And Problem-Solving” (MAPS) approach for smoking cessation among individuals with a history of cervical intraepithelial neoplasia (CIN) or cervical cancer. MAPS is a phone counseling approach designed to facilitate long-term abstinence that comprises 6 counseling calls over 12 months. The current trial is evaluating the efficacy of MAPS+, which comprises all MAPS components plus a 24-month digital treatment adjuvant. This trial represents a logical extension of our previous RCT, which compared the efficacy of MAPS to a quitline control condition and found that MAPS resulted in greater than a 2-fold increase in smoking abstinence at 12 months (i.e., 26.4% vs. 11.9%). This treatment effect was no longer significant at 18 months, suggesting that efficacy dissipated as time from the end of treatment increased. The primary aim of the current trial is to compare the efficacy of MAPS + and ST in facilitating long-term abstinence.MethodsIndividuals who smoke and have a history of cervical cancer or CIN (N = 340) are recruited throughout Florida and randomly assigned to Standard Treatment [ST] or MAPS+. ST participants are electronically connected with the Florida Quitline. MAPS + consists of 6 proactive MAPS-based counseling calls over 12 months plus the novel, personally tailored, text message-based treatment adjuvant delivered over 24 months. All participants receive 12 weeks of combination nicotine replacement therapy (patch and lozenge) and are followed for 24 months. Participant recruitment commenced in December 2022 and is ongoing.DiscussionThis study builds on promising results from our recent trial which found that MAPS was associated with substantially higher abstinence from smoking at the end of the 12-month treatment period. Finding that this low-burden, personally tailored digital treatment adjuvant improves the long-term efficacy of MAPS would have important clinical and public health implications.Trial registrationClinical Trials Registry NCT05645146; https://clinicaltrials.gov/ct2/show/NCT05645146; Registered on December 9, 2022.

Towards logical foundations for probabilistic computation

The overall purpose of the present work is to lay the foundations for a new approach to bridge logic and probabilistic computation. To this aim we introduce extensions of classical and intuitionistic propositional logic with counting quantifiers, that is, quantifiers that measure to which extent a formula is true. The resulting systems, called cCPL and iCPL, respectively, admit a natural semantics, based on the Borel σ-algebra of the Cantor space, together with a sound and complete proof system. Our main results consist in relating cCPL and iCPL with some central concepts in the study of probabilistic computation. On the one hand, the validity of cCPL-formulae in prenex form characterizes the corresponding level of Wagner's hierarchy of counting complexity classes, closely related to probabilistic complexity. On the other hand, proofs in iCPL correspond, in the sense of Curry and Howard, to typing derivations for a randomized extension of the λ-calculus, so that counting quantifiers reveal the probability of termination of the underlying probabilistic programs.

From Non-punctuality to Non-adjacency: A Quest for Decidability of Timed Temporal Logics with Quantifiers

Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are prominent real-time extensions of Linear Temporal Logic (LTL). In general, the satisfiability checking problem for these extensions is undecidable when both the future (Until, U) and the past (Since, S) modalities are used (denoted by MTL[U,S] and TPTL[U,S]). In a classical result, the satisfiability checking for Metric Interval Temporal Logic (MITL[U,S]), a non-punctual fragment of MTL[U,S], is shown to be decidable with EXPSPACE complete complexity. A straightforward adoption of non-punctuality does not recover decidability in the case of TPTL[U,S]. Hence, we propose a more refined notion called non-adjacency for TPTL[U,S] and focus on its 1-variable fragment, 1-TPTL[U,S]. We show that non-adjacent 1-TPTL[U,S] is strictly more expressive than MITL. As one of our main results, we show that the satisfiability checking problem for non-adjacent 1-TPTL[U,S] is decidable with EXPSPACE complete complexity. Our decidability proof relies on a novel technique of anchored interval word abstraction and its reduction to a non-adjacent version of the newly proposed logic called PnEMTL. We further propose an extension of MSO [<] (Monadic Second Order Logic of Orders) with Guarded Metric Quantifiers (GQMSO) and show that it characterizes the expressiveness of PnEMTL. That apart, we introduce the notion of non-adjacency in the context of GQMSO (NA-GQMSO), which is a syntactic generalization of logic Q2MLO due to Hirshfeld and Rabinovich and show the decidability of satisfiability checking for NA-GQMSO.

Forecasting Student Academic Performance Using Neuro-Fuzzy Model

To achieve objective and precise forecasting of students’ academic performance while keeping up with technological improvements and changes, this paper discusses a neuro-fuzzy technique for the prediction of student academic performance. The technique comprises a Neural Network (NN), Fuzzy Logic (FL), Knowledge Base (KB) and Rule Base (RB) subcomponents. The NN subcomponent uses a three-layered feed-forward architecture to acquire a large collection of interconnected units in some pattern for communications. The FL subcomponent is an extension of Boolean logic and it was used for establishing accurate selection processes and precise solutions to multivariable problems. The KB component forms the database of multi-level information while the RB comprises a set of if-then statements for decision-making. The inference engine subcomponent applies a pre-defined procedure on input from the rule base and fuzzy logic interfaces for final prediction. The proposed technique performs predefined procedures that are based on some input sets that store multi-level information derived from several pre-specified scores. Results from the implementation of the technique established its practical function.

From Counterfactual Conditionals to Temporal Conditionals

Although it receives less attention, (Lewis in Noûs 13:455–476, 1979. https://doi.org/10.2307/2215339) admitted that the branching-time(-like) model fits a wide range of counterfactuals, including (Nix) ‘If Nixon had pressed the button, there would have been a nuclear war’, which was raised by (Fine in Mind 84:451–458, 1975). However, Lewis then claimed that similarity analysis is more general than temporality analysis. In this paper, we do not scrutinise his claim. Instead, we re-analyse (Nix) not only model-theoretically but also proof-theoretically from the ‘meaning-as-use’ and ‘inferentialist’ points of view. Then, we re-formalise (Nix) in a natural extension of hybrid tense logic, which we refer to as hybrid tense logic for temporal conditionals (HTL_{TC}). Consequently, we find that not only among counterfactuals, but also among indicatives, there is a wide range of conditionals whose formalisation in HTL_{TC} is appropriate. We refer to these conditionals as temporal conditionals. This suggests a new logical generality that temporality analysis has but similarity analysis does not, from which emerges a new logical perspective on conditionals in general: temporal ones and others.

Situation-Based Connexive Logic

The aim of this paper is to present a system of modal connexive logic based on a situation semantics. In general, modal connexive logics are extensions of standard modal logics that incorporate Aristotle’s and Boethius’ theses, that is the thesis that a sentence cannot imply its negation and the thesis that a sentence cannot imply a pair of contradictory sentences. A key problem in devising a connexive logic is to come up with a system that is both sufficiently strong to fulfill some specific connexive theses and sufficiently well-motivated from a semantical point of view. The approach proposed here tries to address this problem by defining an appropriate connexive relation in terms of more basic notions. The result is a well-motivated system of modal connexive logic that nicely fits in both with the traditional ideas concerning the connexive conditional and with the current developments in connexive logic.

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In the paper we examine the problem of logical systems that are extensions of Classical Propositional Logic with new, intensional connectives of agency: monadic and dyadic bringing it about that. These systems are usually studied within the neighbourhood semantics. Here we propose a different strategy. We study all of the accepted laws and rules of logic of agency and define a translation of the agency operators into connectives interpreted in relating semantics. After this translation we can make a reduction to more basic semantic properties that are required by the particular groups of laws and axioms. Finally, we define proper semantic structures and prove that they are complete with respect to all possible logical systems determined by the combinations of the axioms and rules.