It is a well known empirical observation that natural axiomatic theories are pre-well-ordered by consistency strength. For any natural theory $T$, the next strongest natural theory is $T+\mathsf{Con}_T$. We formulate and prove a statement to the effect that the consistency operator is the weakest natural way to uniformly extend axiomatic theories.

Why are natural theories pre-well-ordered by consistency strength? In previous work, an approach to this question was proposed. This approach was inspired by Martin's Conjecture, one of the most prominent conjectures in recursion theory. Fixing a reasonable subsystem $T$ of arithmetic, the goal was to classify the recursive functions that are monotone with respect to the Lindenbaum algebra of $T$. According to an optimistic conjecture, roughly, every such function must be equivalent to an iterate $\mathsf{Con}_T^\alpha$ of the consistency (...) operator ``in the limit'' within the ultrafilter of sentences that are true in the standard model. In previous work the author established the first case of this optimistic conjecture; roughly, every recursive monotone function is either as weak as the identity operator in the limit or as strong as $\mathsf{Con}_T$ in the limit. Yet in this note we prove that this optimistic conjecture fails already at the next step; there are recursive monotone functions that are neither as weak as $\mathsf{Con}_T$ in the limit nor as strong as $\mathsf{Con}_T^2$ in the limit. In fact, for every $\alpha$, we produce a function that is cofinally equivalent to $\mathsf{Con}^\alpha_T$ yet cofinally equivalent to $\mathsf{Con}_T$. (shrink)

In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency - not necessarily related to (...) the notion of formal consistency. (shrink)

"Paraconsistent Belief Revision Based on a Formal Consistency Operator" delves into Belief Revision—a significant area of research in Formal Philosophy that uses logic to model the ways in which human and artificial agents modify their beliefs in response to new information and examines how these changes can be considered rational. -/- Originally authored as a PhD thesis (previously published in Portuguese), this work provides a novel epistemic interpretation of Paraconsistency through Paraconsistent Belief Revision systems. It explores the concept (...) of paraconsistency from the standpoint of epistemic attitudes of acceptance and rejection. -/- This work challenges the traditional notion that accepting a new belief requires retracting its negation from the current epistemic state. The author contends that such reflexive retraction goes against the principle of informational economy, which is a crucial aspect of rationality in the context of belief change. Consequently, the phenomenon of paraconsistency is further examined from this fresh perspective of belief change, shedding light on the complexities of the Logics of Formal Inconsistency (LFIs). These LFIs provide the foundational logic, offering a comprehensive framework for understanding and implementing paraconsistent principles within belief revision systems. -/- This thesis was supervised by Marcelo Esteban Coniglio and co-supervised by Márcio Moretto Ribeiro, as part of Rafael Rodrigues Testa's doctoral studies at the University of Campinas (Unicamp), Brazil. (shrink)

In order to develop efficient tools for automated reasoning with inconsistency (theorem provers), eventually making Logics of Formal inconsistency (_LFI_) a more appealing formalism for reasoning under uncertainty, it is important to develop the proof theory of the first-order versions of such _LFI_s. Here, we intend to make a first step in this direction. On the other hand, the logic _Ciore_ was developed to provide new logical systems in the study of inconsistent databases from the point of view of _LFI_s. (...) An interesting fact about _Ciore_ is that it has a _strong_ consistency operator, that is, a consistency operator which (forward/backward) propagates inconsistency. Also, it turns out to be an algebraizable logic (in the sense of Blok and Pigozzi) that can be characterized by means of a 3-valued logical matrix. Recently, a first-order version of _Ciore_, namely _QCiore_, was defined preserving the spirit of _Ciore_, that is, without introducing unexpected relationships between the quantifiers. Besides, some important model-theoretic results were obtained for this logic. In this paper we study some proof–theoretic aspects of both _Ciore_ and _QCiore_ respectively. In first place, we introduce a two-sided sequent system for _Ciore_. Later, we prove that this system enjoys the cut-elimination property and apply it to derive some interesting properties. Later, we extend the above-mentioned system to first-order languages and prove completeness and cut-elimination property using the well-known Shütte’s technique. (shrink)

We examine recursive monotonic functions on the Lindenbaum algebra of EA. We prove that no such function sends every consistent φ to a sentence with deductive strength strictly between φ and (φ∧Con(φ)). We generalize this result to iterates of consistency into the effective transfinite. We then prove that for any recursive monotonic function f, if there is an iterate of Con that bounds f everywhere, then f must be somewhere equal to an iterate of Con.

The practice of mathematical word problem is ubiquitous and thought to impact academic achievement. However, the underlying neural mechanisms are still poorly understood. In this study, we investigate how lexical consistency of word problem description is modulated in adults' brain responses during word problem solution. Using functional magnetic resonance imaging methods, we examined compare word problems that included relational statements, such as “A dumpling costs 9 dollars. A wonton is 2 dollars less than a dumpling. How much does a (...) wonton cost?” and manipulated lexical consistency and problem operation. We found a consistency by operation interaction in the widespread fronto-insular-parietal activations, including the anterior insula, dorsoanterior cingulate cortex, middle frontal gyrus, and intraparietal sulcus, such that inconsistent problems engaged stronger activations than consistent problems for addition, whereas the consistency effect was inverse for subtraction. Critically, these results were more salient in the less successful problem solvers than their more successful peers. Our study is the first to demonstrate that lexical consistency effects on arithmetic neural networks are modulated during reading word problem that required distinct arithmetic operations. More broadly, our study has strong potentials to add linkage between neuroscience and education by remediating deficits and enhance instruction design in the school curriculum. (shrink)

El objetivo principal de este artículo es precisar los elementos que operan en el substrato de la filosofía de Thomas Hobbes y que permiten dar coherencia lógica a su sistema. Para ello se apela a la idea de concepto operatorio desarrollada por Eugen Fink, a la vez que se llama la atención sobre la importancia de considerar la filosofía hobbesiana en su totalidad. Esto implica que cualquier análisis de la teoría política de Hobbes debe considerar las relaciones existentes con las (...) concepciones científicas hobbesianas. (shrink)

The South-to-North Water Diversion Project consists of long-distance water delivery channels and a complicated geological environment along the way. To deal with the operation safety of the water conveyance channels in the middle route of the South-to-North Water Diversion Project, this study analyzes six failure modes: structural cracks, poor water delivery during ice periods, instability of canal slopes, material aging, abnormal leakage, and foundation defects. Based on FMEA, a multigranularity language evaluation method that can be converted into interval intuitionistic fuzzy (...) numbers is used to evaluate the severity, occurrence, and detection difficulty of the six failure modes. Interval intuitionistic fuzzy entropy is used to calculate the weights of the risk factors. Finally, a ranking model of each failure mode is built based on the TODIM method. The final ranking results show that the risk of abnormal leakage is the largest, and the risk of poor water delivery during ice periods is the smallest. The feasibility and validity of the calculation results are verified by comparing them with the ranking results of the traditional RPN and TOPSIS methods. The TODIM-FMEA risk assessment model offers a new solution to the problem of risk assessment for water transfer projects. (shrink)

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way as well: (...) to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient toescape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense. (shrink)

Different notions of the consistency of obligations collapse in standard deontic logic. In justification logics, which feature explicit reasons for obligations, the situation is different. Their strength depends on a constant specification and on the available set of operations for combining different reasons. We present different consistency principles in justification logic and compare their logical strength. We propose a novel semantics for which justification logics with the explicit version of axiom D, jd⁠, are complete for arbitrary constant specifications. (...) Consistency is sometimes formulated in terms of permission. We therefore study permission in the context of justification logic, introducing a notion of free-choice permission for the first time. We then discuss the philosophical implications with regard to some deontic paradoxes. (shrink)

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the (...) validity of the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core– in the case studied here, this common core is classical positive propositional logic (CPL + ). The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of logics of formal inconsistency and undeterminedness (LFIUs), namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion at once. The last sections offer an algebraic account for such logics by adapting the swap-structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite non-deterministic matrices. (shrink)

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express metalogical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the logics of formal inconsistency and by the logics of formal undeterminedness. LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the validity of (...) the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core—in the case studied here, this common core is classical positive propositional logic. The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of LFI and undeterminedness, namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion one at a time. The last sections offer an algebraic account for such logics by adapting the swap structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite nondeterministic matrices. (shrink)

In this paper I introduce and develop an approach to tenses and temporal expressions that is a mix between eternalism and temporalism consisting in appeal to ‘variadic operators’. The type of variadic operator I will be concerned with is the expansive variadic operator, which takes as input predicates of a certain adicity and yields new predicates with one additional degree of adicity. Appeal to variadic operators has proven useful in giving the semantics of several types of expressions: adverbs (...) ), prepositional phrases ), relational terms ), etc. The focus of this paper is on tenses and temporal expressions, with the aim of showing how these are treated by appeal to temporal variadic operators. First I define the temporal variadic operator and then show how it can be used to account for simple tensed sentences. I also give a rough sketch of how it can accommodate more complex phenomena like sequence of time, interaction between tenses and temporal adverbials, temporal anaphora, later-than-matrix and double-access readings, etc. (shrink)

Background and significance of research: Nurses’ awareness of professional values and how those values affect their behaviors is an integral part of nursing care. There is a large body of research on nursing professional values, however, a careful survey of the available literature did not yield any studies investigating the status of professional values in operating rooms. Objective: This study aims to investigate the perception of operating room nurses of university hospitals toward professional values. Research plan: In this cross-sectional study, (...) data were collected using Schank and Weis’s Nurses Professional Values Scale–Revised. The collected data were analyzed in SPSS version 16. Participants and settings: The 513 participants of the study consisted of operating room nurses and nurse anesthetists from six university hospitals. Ethical considerations: This study has been approved by the ethics committee of the university. Findings: The mean total professional values score of the operating room staff was found to be 100.84 ± 15.685, which indicates that the participants had a positive perception toward observance of nursing professional values in practice. The results showed that the participants considered the domains of justice and activism as, respectively, the most and the least important. The operating room staff’s overall professional values scores were not found to correlate significantly with their ages, professional experience, university majors, or attendance at ethics workshops. However, a significant difference was found between the professional values scores of the female and male staff. The professional values scores of the operating room nurses and the nurse anesthetists were not significantly different (p value = 0.494). Conclusion: Operating room staff’s awareness of professional values is essential to providing care to patients based on professional principles. Accordingly, there is need for programs to raise operating room nurses’ awareness of their professional duties and improve their professional performance. (shrink)

A series of representations must be semantics-driven if the members of that series are to combine into a single thought: where semantics is not operative, there is at most a series of disjoint representations that add up to nothing true or false, and therefore do not constitute a thought at all. A consequence is that there is necessarily a gulf between simulating thought, on the one hand, and actually thinking, on the other. A related point is that a popular doctrine (...) - the so-called 'computational theory of mind' (CTM) - is based on a confusion. CTM is the view that thought-processes consist in 'computations', where a computation is defined as a 'form-driven' operation on symbols. The expression 'form-driven operation' is ambiguous, as it may refer either to syntax-driven operations or to morphology-driven operations. Syntax-driven operations presuppose the existence of operations that are driven by semantic and extra-semantic knowledge. So CTM is false if the terms 'computation' and 'form-driven operation' are taken to refer to syntax-driven operations. Thus, if CTM is to work, those expressions must be taken to refer to morphology-driven operations. CTM therefore fails, given that an operation must be semantics-driven if it is to qualify as a thought. CTM therefore fails on each possible disambiguation of the expressions 'formal operation' and 'computation,' and it is therefore false. (shrink)

In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish a classical (...) recapture result based on the two logics. In the second part of the paper, we compare the approach in terms of normality operators with an established approach to classical recapture, namely minimal inconsistency. Finally, we discuss technical issues connecting LPe and Ke3 to the tradition of Logics of Formal Inconsistency and Underterminedness. (shrink)

In this work, a virtual submerged floating operational system based on parallel and serial robotic platforms is proposed. The primary aim behind its development lies in carrying out simulated underwater manipulation experiments in an easier and safer way. This VSFOS is consisted of a six-degree-of-freedom parallel platform, an ABB serial manipulator, an inertial sensor, and a real-time industrial computer. The 6-DOF platform is used to simulate the movement of an underwater vehicle, whose attitude is measured by the inertial sensor. The (...) ABB manipulator, controlled by the real-time industrial computer, works as an operational tool to perform underwater manipulation tasks. In the control system architecture, software is developed to receive the data collected by the inertial sensor, to communicate and send instructions. Furthermore, the real-time status of the manipulator is displayed in this software. To validate the proposed system, two experiments have been conducted to test its performance. In the first experiment, the test is carried out to check the communication function of VSFOS, while in the second one, the manipulator is intended to follow the movement of the parallel platform and perform simulated operational task in the space. The obtained results from these two experiments show clearly the effectiveness and the performance of the proposed VSFOS. (shrink)

In this paper, I consider two curious subsystems ofFrege's Grundgesetze der Arithmetik: Richard Heck's predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T in monadic second-order logic, consisting of axiom V and 1 1-comprehension (in a language containing anabstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both Heck (...) and T prove the existence of infinitely many non-logical objects (T deriving,moreover, the nonexistence of the value-range concept). Some implications concerning the interpretation of Frege's proof of referentiality and the possibility of classifying any of these subsystems as logicist are discussed. Finally, I explore the relation of T toCantor's theorem which is somewhat surprising. (shrink)

It is a classic result in modal logic, often referred to as Jónsson-Tarski duality, that the category of modal algebras is dually equivalent to the category of descriptive frames. The latter are Kripke frames equipped with a Stone topology such that the binary relation is continuous. This duality generalizes the celebrated Stone duality for boolean algebras. Our goal is to generalize descriptive frames so that the topology is an arbitrary compact Hausdorff topology. For this, instead of working with the boolean (...) algebra of clopen subsets of a Stone space, we work with the ring of continuous real-valued functions on a compact Hausdorff space. The main novelty is to define a modal operator on such a ring utilizing a continuous relation on a compact Hausdorff space.Our starting point is the well-known Gelfand duality between the category ${\sf KHaus}$ of compact Hausdorff spaces and the category $\boldsymbol {\mathit {uba}\ell }$ of uniformly complete bounded archimedean $\ell $ -algebras. We endow a bounded archimedean $\ell $ -algebra with a modal operator, which results in the category $\boldsymbol {\mathit {mba}\ell }$ of modal bounded archimedean $\ell $ -algebras. Our main result establishes a dual adjunction between $\boldsymbol {\mathit {mba}\ell }$ and the category ${\sf KHF}$ of what we call compact Hausdorff frames; that is, Kripke frames equipped with a compact Hausdorff topology such that the binary relation is continuous. This dual adjunction restricts to a dual equivalence between ${\sf KHF}$ and the reflective subcategory $\boldsymbol {\mathit {muba}\ell }$ of $\boldsymbol {\mathit {mba}\ell }$ consisting of uniformly complete objects of $\boldsymbol {\mathit {mba}\ell }$. This generalizes both Gelfand duality and Jónsson-Tarski duality. (shrink)

It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more (...) encompassing Δ₁¹-comprehension schema would already be inconsistent. In the present paper, we show that this is not the case. (shrink)

Ruth Millikan has hypothesised that human cognition contains ‘consistency testers’. Consistency testers check whether different judgements a thinker makes about the same subject matter agree or conflict. Millikan’s suggestion is that, where the same concept has been applied to the world via two routes, and the two judgements that result are found to be inconsistent, that makes the thinker less inclined to apply those concepts in those ways in the future. If human cognition does indeed include such a (...) capacity, its operation will be an important determinant of how people use concepts. It will have a major impact on which concepts they deploy and which means of application (conceptions) they rely on. Since consistency testers are a selection mechanism at the heart of conceptual thinking, they would be crucial to understanding how concepts are selected – why some are retained and proliferate and others die out. Hence, whether consistency testers for concepts exist, and how they operate, is an important question for those seeking to understand the cultural evolution of concepts, and of the words we use to express them. (shrink)

“Small” large cardinal notions in the language of ZFC are those large cardinal notions that are consistent with V = L. Besides their original formulation in classical set theory, we have a variety of analogue notions in systems of admissible set theory, admissible recursion theory, constructive set theory, constructive type theory, explicit mathematics and recursive ordinal notations (as used in proof theory). On the face of it, it is surprising that such distinctively set-theoretical notions have analogues in such disaparate and (...) relatively constructive contexts. There must be an underlying reason why that is possible (and, incidentally, why “large” large cardinal notions have not led to comparable analogues). My long term aim is to develop a common language in which such notions can be expressed and can be interpreted both in their original classical form and in their analogue form in each of these special constructive and semi-constructive cases. This is a program in progress. What is done here, to begin with, is to show how that can be done to a considerable extent in the settings of classical and admissible set theory (and thence, admissible recursion theory). The approach taken here is to expand the language of set theory to allow us to talk about (possibly partial) operations applicable both to sets and to operations and to formulate the large cardinal notions in question in terms of operational closure conditions; at the same time only minimal existence axioms are posited for sets. The resulting system, called Operational Set Theory, is a partial adaptation to the set-theoretical framework of the explicit mathematics framework Feferman (1975). The.. (shrink)

This paper discusses a dualization of Fitting's notion of a "cut-down" operation on a bilattice, rendering a "track-down" operation, later used to represent the idea that a consistent opinion cannot arise from a set including an inconsistent opinion. The logic of track-down operations on bilattices is proved equivalent to the logic d_Sfde, dual to Deutsch's system S_fde. Furthermore, track-down operations are employed to provide an epistemic interpretation for paraconsistent weak Kleene logic. Finally, two logics of sequential combinations of cut-and track-down (...) operations allow settling positively the question of whether bilattice-based semantics are available for subsystems of S_fde. (shrink)

The study of structure systems, an abstraction of the concept of first-order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first-order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality-free first-order structures are provided in the framework of structure systems. (© 2007 (...) WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

The study aimed to identify the intermediate role of the standard of operations in the relationship between the focus on students and beneficiaries in achieving satisfaction of students in Palestinian universities. The study used the analytical descriptive method. The study was conducted on university leadership in Al-Azhar, Islamic and Al-Aqsa Universities. The study sample consisted of (200) individuals, 182 of whom responded, and the questionnaire was used in collecting the data. The results of the study were as follows: - There (...) is a statistically significant effect on the adoption of the criterion of focus on the students benefiting to achieve the satisfaction of students in the Palestinian universities, where the value of R Square (35.3%), there is a statistically significant effect on the adoption of the criterion of focus on the students benefiting on the use of the standard of operations in Palestinian universities. The value of the R Square is (62.8%), there is a statistically significant impact of the criterion of operations on the satisfaction of students in Palestinian universities. Where the value of the R is (36.2%), there is a significant effect on the adoption of the criterion of emphasis on students benefiting from the satisfaction of students in Palestinian universities with the existence of the standard of operations as an intermediary variable. The role of the mediator in the relationship between the adoptions of the criterion of focus on the students benefiting to achieve the satisfaction of students in Palestinian universities was revealed through the use of Path Analysis. The study presented a number of recommendations, the most important of which is: to increase the focus of the universities on students and beneficiaries in a manner appropriate to achieve the objectives of the university on the one hand, and students and beneficiaries on the other, and in line with the approach of quality and excellence, the universities more attention to the management of operations through the design and development of programs Academic and internal services according to the needs of students, and improving processes in innovative ways to generate added value for students and beneficiaries, the universities have made more efforts to create satisfaction among students and beneficiaries by developing internal performance indicators to measure student satisfaction, Students and other university beneficiaries periodically to improve their satisfaction. (shrink)

This article describes a benchmarking tool managers can use to determine operational policies and processes that could enhance an organization's social and ethical performance. The benchmarking tool consists of a 13‐dimension, 110‐item survey based on an Optimal Ethics Systems Model. These best practices in business ethics are derived from an analysis and assessment of seven institutional infrastructures and accountability standards developed to help managers improve organizational social and ethical performance.

Summary The analysis of structures of argumentation in historical controversies is considered to be a basic contribution to the dynamics of theories. In this paper attention is drawn to the occurence of operational arguments in the history of physics. This is to be discussed especially in respect to the nineteenth-century debates on the consistency of Wilhelm Weber's electrodynamic law with the principle of conservation of energy.

Hull et al.'s analysis of operant behavior in terms of interaction and replication does not seem consistent with a genuine selection model. The putative replicators do not replicate, and the overall process is more reminiscent of directed mutation than of natural selection. General analogies between natural selection and operant reinforcement are too superficial to be of much scientific use.

Samir Okasha argues that clade selection is an incoherent concept, because the relation that constitutes clades is such that it renders parent-offspring (reproduction) relations between clades impossible. He reasons that since clades cannot reproduce, it is not coherent to speak of natural selection operating at the clade level. We argue, however, that when species-level lineages and clade-level lineages are treated consistently according to standard cladist commitments, clade reproduction is indeed possible and clade selection is coherent if certain conditions obtain. Despite (...) clade selection's logical coherence, however, we share some of Okasha's pessimism. Whether or not clades are a unit of selection is ultimately a question of empirical support and theoretical import. (shrink)

Restorative justice conferences that operate as sentencing mechanisms involve the making of a trade-off between empowering lay participants to make their own decisions, and the requirements of consistency and proportionality, which are established principles of sentencing. In current restorative justice practice, this trade-off tends to be made more in favour of consistency and proportionality, at the expense of the empowerment of lay participants.Empowerment is central to key benefits of restorative justice, such as reducing recidivism and increasing victim satisfaction. (...) However, its importance to the effectiveness of restorative justice is not always properly acknowledged. In addition to this lack of acknowledgment, there are both conceptual and practical problems with the principles of consistency and proportionality (particularly in the way that they are presented when considered in relation to restorative justice) that are often overlooked. As a result, the tendency is for assumptions to be made about the necessary supremacy of these principles over empowerment. This paper urges more acknowledgement of the importance of empowerment in restorative justice, together with a greater appreciation of the problems with consistency and proportionality, with a view to challenging assumptions about the way that the trade-off must be made. (shrink)

This work considers the formalisation of the merging process of stratified belief bases, where beliefs are stored in different layers or strata. Their strata are ranked, following a total order, employing the value the agent using the belief base assigns to these beliefs. The agent uses an argumentation mechanism to reason from the belief base and obtain the final inferences. We present two ways of merging stratified belief bases: the first is defined by merging two strata without belief preservation, and (...) the second by merging two strata with belief preservation. For these operators, as layers merge, it is possible that some information has to be deleted from the stratum to maintain consistency. The latter merge operator will be defined as performing their actions so that information removed from the stratum is preserved after the merging by moving it to a stratum containing information perceived as having a lower value and where those beliefs may trigger a new revision, possibly starting a cascading effect. (shrink)

Operative grace is generally considered to be a paradigm example of special divine action. In this paper, we suggest one reason to think operative grace might be consistent with general divine action alone. On our view, then, a deist can consistently believe in a doctrine of saving faith.

In the consistent histories formalism one specifies a family of histories as an exhaustive set of pairwise exclusive descriptions of the dynamics of a quantum system. We define branching families of histories, which strike a middle ground between the two available mathematically precise definitions of families of histories, viz., product families and Isham’s history projector operator formalism. The former are too narrow for applications, and the latter’s generality comes at a certain cost, barring an intuitive reading of the “histories”. (...) Branching families retain the intuitiveness of product families, they allow for the interpretation of a history’s weight as a probability, and they allow one to distinguish two kinds of coarse-graining, leading to reconsidering the motivation for the consistency condition. (shrink)

We consider the first-order finite-difference expression of the commutator between d / dx and x. This is the appropriate setting in which to propose commutators and time operators for a quantum system with an arbitrary potential function and a discrete energy spectrum. The resulting commutators are identified as universal lowering and raising operators. We also find time operators which are finite-difference derivations with respect to the energy. The matrix elements of the commutator in the energy representation are analyzed, and we (...) find consistency with the equality \. We apply the theory to the particle in an infinite well and for the Harmonic oscillator as examples. (shrink)

Alain Badiou’s reception in the English-speaking world has centred on his project of a “mathematical ontology” undertaken in Being and Event. Its reception has raised serious concerns about how mathematics could be relevant to concrete situations. Caution must be taken in applying mathematics to concrete situationsand, without making explicit the equivocal senses of “consistency” as it operates in Badiou’s thought, this caution cannot be precisely applied. By examining Being and Event as well as looking backwards at his first philosophical (...) work, The Concept of Model, some key distinctions on the meaning of “consistency” will be clarified. (shrink)

Within the field of human‐computer interaction, the study of the interaction between people and computers has revealed many phenomena. For example, highly interactive devices, such as the Apple Macintosh, are often easier to learn and use than keyboard‐based devices such as Unix. Similarly, consistent interfaces are easier to learn and use than inconsistent ones. This article describes an integrated cognitive model designed to exhibit a range of these phenomena while learning task‐action mappings: action sequences for achieving simple goals, such as (...) opening a file in a word processor. The model, called TAL, is of a user who is familiar with the basic operations of a keyboard and mouse, but unfamiliar with the particular menu structures, words, and actions required to use the device. The model is constructed in Soar and employs a single set of architectural mechanisms. It exhibits behavior that captures human preference for consistent, interactive, and meaningful task‐action mappings. (shrink)

The equivalence principle, being one of the building blocks of general relativity, seems to be crucial for analysis of quantum effects in gravity. In this paper we consider the relation between the equivalence principle and the consistency of quantum information processing in gravitational field. We propose an analysis with a looped evolution consisting of steps both in the gravitational field and in the accelerated reference frame. We show that without the equivalence principle the looped quantum evolution cannot be unitary (...) and looses its consistency. For this reasoning the equivalence principle is formulated in terms of the gauge transformations and is analyzed for particles acquiring an appropriate phase associated with the action over the looped path. In consequence, to keep consistency of quantum operations in gravitational field, it is required to keep a quantum variant of the equivalence principle. This proves importance of the quantized version of this fundamental gravitational principle for quantum information processing. (shrink)

In his Tractatus, Wittgenstein maintained that arithmetic consists of equations arrived at by the practice of calculating outcomes of operations$\Omega ^{n}(\bar {\xi })$defined with the help of numeral exponents. Since$Num$(x) and quantification over numbers seem ill-formed, Ramsey wrote that the approach is faced with “insuperable difficulties.” This paper takes Wittgenstein to have assumed that his audience would have an understanding of the implicit general rules governing his operations. By employing the Tractarian logicist interpretation that theN-operator$N(\bar {\xi })$and recursively defined (...) arithmetic operators$\Omega ^{n}(\bar {\xi })$are not different in kind, we can address Ramsey’s problem. Moreover, we can take important steps toward better understanding how Wittgenstein might have imagined emulating proof by mathematical induction. (shrink)

The Wigner–Weyl mapping of quantum operators to classical phase space functions preserves the algebra, when operator multiplication is mapped to the binary “*” operation. However, this isomorphism is destroyed under the quasiclassical substitution of * with conventional multiplication; consequently, an approximate mapping is required if algebraic relations are to be preserved. Such a mapping is uniquely determined by the fundamental relations of quantum mechanics, as is shown in this paper. The resultant quasiclassical approximation leads to an algebraic derivation of (...) Thomas–Fermi theory, and a new quantization rule which—unlike semiclassical quantization—is non-invariant under action transformations of the Hamiltonian, in the same qualitative manner as the true eigenvalues. The quasiclassical eigenvalues are shown to be significantly more accurate than the corresponding semiclassical values, for a variety of 1D and 2D systems. In addition, certain standard refinements of semiclassical theory are shown to be easily incorporated into the quasiclassical formalism. (shrink)

Spin is a fundamental and distinctive property of the electron, having far-reaching implications. Yet its purely formal treatment often blurs the physical content and meaning of the spin operator and associated observables. In this work we propose to advance in disclosing the meaning behind the formalism, by first recalling some basic facts about the one-particle spin operator. Consistently informed by and in line with the quantum formalism, we then proceed to analyse in detail the spin projection operator (...) correlation function \=\left\langle \left \left \right\rangle \) for the bipartite singlet state, and show it to be amenable to an unequivocal probabilistic reading. In particular, the calculation of \\) entails a partitioning of the probability space, which is dependent on the directions \.\) The derivation of the CHSH- or other Bell-type inequalities, on the other hand, does not consider such partitioning. This observation puts into question the applicability of Bell-type inequalities to the bipartite singlet spin state. (shrink)

As argued in Hellman (1993), the theorem of Pour-El and Richards (1983) can be seen by the classicist as limiting constructivist efforts to recover the mathematics for quantum mechanics. Although Bridges (1995) may be right that the constructivist would work with a different definition of 'closed operator', this does not affect my point that neither the classical unbounded operators standardly recognized in quantum mechanics nor their restrictions to constructive arguments are recognizable as objects by the constructivist. Constructive substitutes that (...) may still be possible necessarily involve additional 'incompleteness' in the mathematical representation of quantum phenomena. Concerning a second line of reasoning in Hellman (1993), its import is that constructivist practice is consistent with a 'liberal' stance but not with a 'radical', verificationist philosophical position. Whether such a position is actually espoused by certain leading constructivists, they are invited to clarify. (shrink)

The study aims to contribute to understand the Vitruvian design system through the analysis of the temples described in the text leading to the three key concepts related: proportio, commensus and commodulatio. At first, it is proposed a conceptual discussion about the origin of the compositional elements, and further it is discussed the concept of proportio as an operation of sizing and scaling these elements individually. Analyzed the definition and types of elements, it is proposed to continue the discussion on (...) the relationship that must be built as a way of associating elements in a consistent way, leading to the notion of symmetria, understood as an ideal state in which the elements maintain dimensional and/or geometrical relationships between them, creating a relational harmony. From the operational point of view, it is sought to demonstrate that the Vitruvian symmetria is fetched from two types of relations: a modular and a dimensional. (shrink)

In this paper we show that the Proper Forcing Axiom is preserved under forcing over any poset PP with the following property: In the generalized Banach–Mazur game over PP of length , Player II has a winning strategy which depends only on the current position and the ordinal indicating the number of moves made so far. By the current position we mean: The move just made by Player I for a successor stage, or the infimum of all the moves made (...) so far for a limit stage. As a consequence of this theorem, we introduce a weak form of the square principle and show that it is consistent with PFA. (shrink)

As an extension of the traditional theory of the syllogism, Leibniz’s algebra of concepts is built up from the term-logical operators of conjunction, negation, and the relation of containment.Leibniz’s laws of consistency state that no concept contains its own negation, and that if concept A contains concept B, then A cannot also contain Not-B. Leibniz believed that these principles would be universally valid, but he eventually discovered that they have to be restricted to self-consistent concepts.This result is of utmost (...) importance for the philosophical foundations of connexive logic, i.e. for the question how far either “Aristotle’s Thesis”, ¬(α → ¬α), or “Boethius’s Thesis”, (α → β) → ¬(α → ¬β), should be accepted as reasonable principles of a logic of conditionals. (shrink)

We treat emergence via reference to four ideas: (1) the different levels of emergence are characterised by distinct conservation laws, (2) the emergence process starts from some instability, (3) the driving force of emergence is given by selection processes allowing canalisation of specific (emerging) paths, and (4) new forms of stability are determined by new kinds of operations. At a quantum-mechanical level entropy is conserved in an isolated system or at global level and the only allowed operations are local shifts (...) in order and disorder – that implies weakening and strengthening correlations. The stable state is here represented by a highly symmetric state. Emergence of the classical physical world arises when energy is conserved and allowable operations include building and breaking of physical-chemical connections. The stable state is here the energy minimum. Emergence of the biotic world implies that the conserved quantity is energy efficiency. Energy is no longer locally conserved. The allowed operations are those that are consistent with the survival (persistence) of the organism. The emergence of the mind is grounded in selecting those operations that are rational (in the sense of maintaining biological self-organisation). Here, the rational value of behaviour is the quantity of interest. Mounting the ladder of (both cosmic and biological) evolution means to have more and more selection of the possible outcomes (and therefore of the relative operations) but in a growing space of possibilities: if selection would reduce more and more the space of possibilities, the final result would be a rigid order; at the other extreme, if we had only expansion of the possibilities without selection, the final result would be disorder. So growing complexity can be understood as a path in the evolutionary landscape of the systems in which a balance of order and disorder is maintained although each level emerges as a result of the selection. (shrink)

We study a modal language for negative operators—an intuitionistic-like negation and its paraconsistent dual—added to (bounded) distributive lattices. For each non-classical negation an extra operator is hereby adjoined in order to allow for standard logical inferences to be opportunely restored. We present abstract characterizations and exhibit the main properties of each kind of negative modality, as well as of the associated connectives that express consistency and determinedness at the object-language level. Appropriate sequent-style proof systems and adequate kripke semantics (...) are also introduced, characterizing the minimal normal logic and a few other basic logics containing such negative modalities and their companions. (shrink)