A Double Deduction System for Quantum Logic Based On Natural Deduction

The author presents a deduction system for Quantum Logic. This system is a combination of a natural deduction system and rules based on the relation of compatibility. This relation is the logical correspondant of the commutativity of observables in Quantum Mechanics or perpendicularity in Hilbert spaces.Contrary to the system proposed by Gibbins and Cutland, the natural deduction part of the system is pure: no algebraic artefact is added. The rules of the system are the rules of Classical Natural Deduction in which is added a control of contexts using the compatibility relation.The author uses his system to prove the following theorem: if propositions of a quantum logical propositional calculus system are mutually compatible, they form a classical subsystem.     

Substructural Logics in Natural Deduction

Extensions of Natural Deduction to Substructural Logics of IntuitionisticLogic are shown: Fragments of Intuitionistic Linear, Relevantand BCK Logic. Rules for implication, conjunction, disjunctionand falsum are defined, where conjunction and disjunction respectcontexts of assumptions. So, conjunction and disjunction areadditive in the terminology of linear logic. Explicit contractionand weakening rules are given. It is shown that conversionsand permutations can be adapted to all these rules, and thatweak normalisation and subformula property holds. The resultsgeneralise to quantification.     

The Neglect of Epistemic Considerations in Logic: The Case of Epistemic Assumptions

The two different layers of logical theory—epistemological and ontological—are considered and explained. Special attention is given to epistemic assumptions of the kind that a judgement is granted as known, and their role in validating rules of inference, namely to aid the inferential preservation of epistemic matters from premise judgements to conclusion judgement, while ordinary Natural Deduction assumptions (that propositions are true) serve to establish the holding of consequence from antecedent propositions to succedent proposition.

     

Harmonising natural deduction

Prawitz proved a theorem, formalising ‘harmony’ in Natural Deduction systems, which showed that, corresponding to any deduction there is one to the same effect but in which no formula occurrence is both the consequence of an application of an introduction rule and major premise of an application of the related elimination rule. As Gentzen ordered the rules, certain rules in Classical Logic had to be excepted, but if we see the appropriate rules instead as rules for Contradiction, then we can extend the theorem to the classical case. Properly arranged there is a thoroughgoing ‘harmony’, in the classical rules. Indeed, as we shall see, they are, all together, far more ‘harmonious’ in the general sense than has been commonly observed. As this paper will show, the appearance of disharmony has only arisen because of the illogical way in which natural deduction rules for Classical Logic have been presented.     

Expressive Power and Incompleteness of Propositional Logics

Natural deduction systems were motivated by the desire to define the meaning of each connective by specifying how it is introduced and eliminated from inference. In one sense, this attempt fails, for it is well known that propositional logic rules (however formulated) underdetermine the classical truth tables. Natural deduction rules are too weak to enforce the intended readings of the connectives; they allow non-standard models. Two reactions to this phenomenon appear in the literature. One is to try to restore the standard readings, for example by adopting sequent rules with multiple conclusions. Another is to explore what readings the natural deduction rules do enforce. When the notion of a model of a rule is generalized, it is found that natural deduction rules express “intuitionistic” readings of their connectives. A third approach is presented here. The intuitionistic readings emerge when models of rules are defined globally, but the notion of a local model of a rule is also natural. Using this benchmark, natural deduction rules enforce exactly the classical readings of the connectives, while this is not true of axiomatic systems. This vindicates the historical motivation for natural deduction rules. One odd consequence of using the local model benchmark is that some systems of propositional logic are not complete for the semantics that their rules express. Parallels are drawn with incompleteness results in modal logic to help make sense of this.     

On Argumentation Logic and Propositional Logic

This paper studies the relationship between Argumentation Logic (AL), a recently defined logic based on the study of argumentation in AI, and classical Propositional Logic (PL). In particular, it shows that AL and PL are logically equivalent in that they have the same entailment relation from any given classically consistent theory. This equivalence follows from a correspondence between the non-acceptability of (arguments for) sentences in AL and Natural Deduction (ND) proofs of the complement of these sentences. The proof of this equivalence uses a restricted form of ND proofs, where hypotheses in the application of the Reductio of Absurdum inference rule are required to be “relevant” to the absurdity derived in the rule. The paper also discusses how the argumentative re-interpretation of PL could help control the application of ex-falso quodlibet in the presence of inconsistencies.     

Mental powers and the soul in Kant’s Subjective Deduction and the Second Paralogism

Kant’s claim in the Subjective Deduction that we have multiple fundamental mental powers appears to be susceptible to some a priori metaphysical arguments made against multiple fundamental mental powers by Christian Wolff who held that these powers would violate the unity of thought and entail that the soul is an extended composite. I argue, however, that in the Second Paralogism and his lectures on metaphysics, Kant provides arguments that overcome these objections by showing that it is possible that a composite could ground the unity of thought, that properties are powers and therefore the soul could possess multiple powers, and the soul is a thing in itself so it cannot be an extended composite. These arguments lend additional support to the attribution of multiple mental powers to us in the Subjective Deduction.     

Nonconceptualism,Hume’s Problem,and the Deduction

Lucy Allais seeks to provide a reading of the Transcendental Deduction of the Categories which is compatible with a nonconceptualist account of Kant’s theory of intuition. According to her interpretation, the aim of the Deduction is to show that a priori concept application is required for empirical concept application. I argue that once we distinguish the application of the categories from the instantiation of the categories, we see that Allais’s reconstruction of the Deduction cannot provide an answer to Hume’s problem about our entitlement to use a priori concepts when thinking about the objects of empirical intuition. If the Deduction is to provide a response to Hume, Allais’s interpretation must be rejected.     

Interactions entre règles sociales de santé publique : étude des liens entre le port du masque et les règles routières en temps de crise sanitaire

IntroductionThe health crisis that France has experienced since the beginning of 2020 has justified the introduction of new health rules requiring changes in behaviour. The context of the implementation of these health rules, instituted very recently and for a limited period of time, raises the question of their perception and respect among the population.ObjectiveMobilising the social developmental psychology, the objective of this article is to explore inter-individual differences in the perception of these health rules measured through the wearing of masks. It aims also at studying the links between these perceptions with the experience of the health context and the perception of other legal public health rules, apprehended through some road safety rules.MethodThe questionnaire survey, carried out during the second confinement with a representative sample of 4999 people, made it possible to measure the experience of the health context, the internalisation of the rules and their justifications, the usefulness of the rules and the perception of the legal system.ResultsThe results show the links between internalisation, the type of arguments used to justify it for wearing a mask and for road rules respectively, as well as the links between internalisation and the perception of the legal system. They also show that women use moral and prudential arguments more to justify their internalisation of rules and that they have internalised the traffic rules (but not the wearing of masks) more than men.ConclusionThese results show that the perception of the rule of wearing a mask is more related to the general perception that individuals have of the legal system and other legal public health rules involving the relationship with others than to the context in which these rules were put in place.     

The Second Step of the B‐Deduction

This paper offers a new interpretation of Kant's puzzling claim that the B‐Deduction in the Critique of Pure Reason should be considered as having two main steps. Previous commentators have tended to agree in general on the first step as arguing for the necessity of the categories for possible experience, but disagree on what the second step is and whether Kant even needs a second step. I argue that the two parts of the B‐Deduction correspond to the two aspects of a priori cognition: necessity and universality. The bulk of the paper consists of support for the second step, the universality of the categories. I show that Kant's arguments in the second half of the B‐Deduction aim to define the scope of that universality for possible experience by considering the possibilities of divine intellectual intuition, of non‐human kinds of sensible intuition, and of apperception of the self. In these ways Kant delimits the boundaries of the applicability of the categories and excludes any other possible experience for human beings.     

Stoic Sequent Logic and Proof Theory

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness.     

Resources,Rules, and Oppression

There is a large and growing literature on communal interpretive resources: the concepts, theories, narratives, and so on that a community draws on in interpreting its members and their world. (They’re also called “hermeneutical resources” in some places and “epistemic resources” in others.) Several recent contributions to this literature have concerned dominant and resistant interpretive resources and how they affect concrete lived interactions. In this article, I note that “using” interpretive resources—applying them to parts of the world in conversation with others—is “a rule‐governed activity”; and I propose that in oppressive systems, these rules are influenced by the rules of oppression. Section I clarifies some rules governing the use of resources. Section II draws on work by Gaile Pohlhaus, Jr. and others to suggest that according to the present rules of our oppressive system, it is permissible for dominantly situated speakers to dismiss interpretive resources developed in marginalized communities. Section III appeals to Charles Mills’s work on White ignorance to propose, further, that our system’s rules make it impermissible and deserving of punishment to use resistant resources. The conclusion enumerates several further points about such rules governing the use of interpretive resources, their social effects, and some philosophical literatures.     

Kant and Kantian Themes in Recent Analytic Philosophy

This article notes six advances in recent analytic Kant research: (1) Strawson's interpretation, which, together with work by Bennett, Sellars, and others, brought renewed attention to Kant through its account of space, time, objects, and the Transcendental Deduction and its sharp criticisms of Kant on causality and idealism; (2) the subsequent investigations of Kantian topics ranging from cognitive science and philosophy of science to mathematics; (3) the detailed work, by a number of scholars, on the Transcendental Deduction; (4) the clearer understanding of transcendental idealism sparked by reactions to Allison's epistemic account; (5) the resulting need—prompted also by new studies of the thing in itself—to face up to the old question of the philosophical defensibility of such idealism; and (6) the active engagement with Kant's ethics and political philosophy that derives from Rawls's and others' work.     

Fate and the Fortune of the Categories: Kant on the Usurpation and Schematization of Concepts

In the early steps of the Transcendental Deduction in the Critique of Pure Reason, Kant briefly addresses the threat posed by usurpatory concepts such as ‘fate’ and ‘fortune’. Commentators have largely passed over these remarks, but in this paper I argue that a careful analysis of the reasons why ‘fate’ and ‘fortune’ are usurpatory reveals an important point about the relation between the Deduction and the Principles chapters of the Critique. In particular, I argue that ‘fate’ and ‘fortune’ are usurpatory because they are unable to discriminate between the particular contents of experience, and that this requires that Kant provide an account of how the categories are able to accomplish this task. And this in turn shows that the justificatory work begun in the Deduction can be completed only in the Schematism and Principles.     

A reasoning method for a paraconsistent logic

A proof method for automation of reasoning in a paraconsistent logic, the calculus C1* of da Costa, is presented. The method is analytical, using a specially designed tableau system. Actually two tableau systems were created. A first one, with a small number of rules in order to be mathematically convenient, is used to prove the soundness and the completeness of the method. The other one, which is equivalent to the former, is a system of derived rules designed to enhance computational efficiency. A prototype based on this second system was effectively implemented.     

The aimless rationality of science 1

It is usually attempted teleologically to demonstrate the rationality of the so‐called scientific method. Goals or aims are posited (and their specification defended) and it is then argued that conformity with some body of methodological rules is conducive to the realization of these goals or aims. A ‘ deontological’ alternative to this approach is offered, adapting insights of contemporary political philosophers, especially John Rawls and Bruce Ackerman. The ‘circumstances of method’ are defined as those circumstances in which it alone makes sense to seek some method for the resolution of disputed issues. It is then shown that individuals who find themselves in these circumstances have reason to conduct themselves in conformity with certain simple rules of argumentation—have reason, indeed, in the very fact that they do so find themselves and altogether without reference to any goals or aims which it might be hoped to achieve. These rules require non‐interference, responsiveness, relevance, and publicity, and are, arguably, the rules which define the concept (and which therefore provide a framework for various conceptions,) of scientific method.     

FNDSB: A fuzzy-neuro decision support system for back pain diagnosis

Back pain is a common pain felt in the back. In the world, it is the fifth common reason for physician visits and in the U.S. about 90% of human adults have back pain at some time in their life. In this paper, we proposed a decision support system for intelligent diagnosis of back pain using a fuzzy-neuro technique to manage the fuzzy concepts. It is also provide an intelligent decision support platform that can assist physicians to diagnose and produce accurate medical advices. The proposed system consists of a user interface that receive symptoms and produce accurate diagnosis with its severity, a fuzzy inference system which contains the strategies of reasoning process based on fuzzification and defuzzification techniques, a fuzzy-neuro system that composed of neural network with fuzzy logic concepts, and a knowledge base which collects of linguistic fuzzy rules. The FNDSB describe knowledge acquisition and representation methods, a way of production linguistic fuzzy rules organization, fuzzification and defuzzification of clinical parameters as input and output values using a Triangular Membership Function (TMF) and Centroid of Area (CoA) techniques respectively. The FNDSB was evaluated using a case study of 10 patients from Al-diwaniyah teaching hospital. According to the evaluation results the system performance around 83.6% efficiency in producing accurate back pain diagnosis.     

Scientific Research and the Public Trust

This essay analyzes the concept of public trust in science and offers some guidance for ethicists, scientists, and policymakers who use this idea defend ethical rules or policies pertaining to the conduct of research. While the notion that public trusts science makes sense in the abstract, it may not be sufficiently focused to support the various rules and policies that authors have tried to derive from it, because the public is not a uniform body with a common set of interests. Well-focused arguments that use public trust to support rules or policies for the conduct of research should specify (a) which public is being referred to (e.g. the general public or a specific public, such as a particular community or group); (b) what this public expects from scientists; (c) how the rule or policy will ensure that these expectations are met; and (d) why is it important to meet these expectations.     

On Kant's Conception of Inner Sense: Self‐Affection by the Understanding

Among the extensive literature on the first Critique, very few commentators offer a thorough analysis of Kant's conception of inner sense. This is quite surprising since the notion is central to Kant's theoretical philosophy, and it is very difficult to provide a consistent interpretation of this notion. In this paper, I first summarize Kant's claims about inner sense in the Transcendental Aesthetic and show why existing interpretations have been unable to dissolve the tensions arising from the conjunction of these claims. Secondly, I present my own reconstruction of Kant's model of inner sense, relying essentially on Kantian considerations found in the B‐version of the Transcendental Deduction. My main idea is that inner sense, for Kant, is a passive faculty that gets affected by the understanding performing its figurative synthesis on material given in outer sense. In the remainder of the paper, I highlight a few consequences of my interpretation and outline ways to deal with some objections.