Equivalents of Mingle and Positive Paradox

Relevant logic is a proper subset of classical logic. It does not include among its theorems any ofpositive paradox A (B A)mingle A (A A)linear order (A B) (B A)unrelated extremes (A ) (B B¯)This article shows that those four formulas have different effects when added to relevant logic, and then lists many formulas that have the same effect as positive paradox or mingle.     

Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

Forms of Quantum Nonseparability and Related Philosophical Consequences

Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is viewed as a consequence of the Hilbert-space quantum mechanical formalism, avoiding thus any direct recourse to the ramifications of Kochen-Specker’s argument or Bell’s inequality. Depending on the mode of assignment of states to physical systems – unit state vectors versus non-idempotent density operators – we distinguish between strong/relational and weak/deconstructional forms of quantum nonseparability. The origin of the latter is traced down and discussed at length, whereas its relation to the all important concept of potentiality in forming a coherent picture of the puzzling entangled interconnections among spatially separated systems is also considered. Finally, certain philosophical consequences of quantum non-separability concerning the nature of quantum objects, the question of realism in quantum mechanics, and possible limitations in revealing the actual character of physical reality in its entirety are explored.     

Negative Equivalence of Extensions of Minimal Logic

Two logics L₁ and L₂ are negatively equivalent if for any set of formulas X and any negated formula ¬, ¬ can be deduced from the set of hypotheses X in L₁ if and only if it can be done in L₂. This article is devoted to the investigation of negative equivalence relation in the class of extensions of minimal logic.The author acknowledges support by the Alexander von Humboldt-StiftungPresented by Jacek Malinowski     

Interactions between Knowledge,Action and Commitment within Agent Dynamic Logic

This paper considers a new class of agent dynamic logics which provide a formal means of specifying and reasoning about the agents activities and informational, motivational and practical aspects of the behaviour of the agents. We present a Hilbert-style deductive system for a basic agent dynamic logic and consider a number of extensions of this logic with axiom schemata formalising interactions between knowledge and commitment (expressing an agent s awareness of her commitments), and interactions between knowledge and actions (expressing no learning and persistence of knowledge after actions). The deductive systems are proved sound and complete with respect to a Kripke-style semantics. Each of the considered logics is shown to have the small model property and therefore decidable.Presented by Ewa Orlowska     

On Alternative Geometries,Arithmetics, and Logics; a Tribute to Łukasiewicz

The paper discusses the similarity between geometry, arithmetic, and logic, specifically with respect to the question of whether applied theories of each may be revised. It argues that they can - even when the revised logic is a paraconsistent one, or the revised arithmetic is an inconsistent one. Indeed, in the case of logic, it argues that logic is not only revisable, but, during its history, it has been revised. The paper also discusses Quine's well known argument against the possibility of logical deviancy.     

Categorical Abstract Algebraic Logic Metalogical Properties

Metalogical properties that have traditionally been studied in the deductive system context (see, e.g., [21]) and transferred later to the institution context [33], are here formulated in the -institution context. Preservation under deductive equivalence of -institutions is investigated. If a property is known to hold in all algebraic -institutions and is preserved under deductive equivalence, then it follows that it holds in all algebraizable -institutions in the sense of [36].     

The Ethics of Type 1 Diabetes Prediction and Prevention Research

There are approximately one million cases oftype 1 diabetes in the US, and the incidenceis increasing worldwide. Given that two-thirdsof cases present in childhood, it is criticalthat prediction and prevention research involvechildren. In this article, I examine whethercurrent research methodologies conform to theethical guidelines enumerated by the NationalCommission for the Protection of Human Subjectsof Biomedical and Behavioral Research, andadopted into the federal regulations thatprotect research subjects. I then offer twopolicy recommendations to help researchersdesign studies that conform to these ethicalrequirements.     

Argumentation and Evidence

This essay explores the role of informal logicand its application in the context of currentdebates regarding evidence-based medicine. This aim is achieved through a discussion ofthe goals and objectives of evidence-basedmedicine and a review of the criticisms raisedagainst evidence-based medicine. Thecontributions to informal logic by StephenToulmin and Douglas Walton are explicated andtheir relevance for evidence-based medicine isdiscussed in relation to a common clinicalscenario: hypertension management. This essayconcludes with a discussion on the relationshipbetween clinical reasoning, rationality, andevidence. It is argued that informal logic hasthe virtue of bringing explicitness to the roleof evidence in clinical reasoning, and bringssensitivity to understanding the role ofdialogical context in the need for evidence inclinical decision making.     

Logic and Aggregation

Paraconsistent logic is an area of philosophical logic that has yet to find acceptance from a wider audience. The area remains, in a word, disreputable. In this essay, we try to reassure potential consumers that it is not necessary to become a radical in order to use paraconsistent logic. According to the radicals, the problem is the absurd classical account of contradiction: Classically inconsistent sets explode only because bourgeois classical semantics holds, in the face of overwhelming evidence to the contrary, that both A and A cannot simultaneously be true! We suggest (more modestly) that there is, at least sometimes, something else worth preserving, even in an inconsistent, unsatisfiable premise set. In this paper we present, in a new guise, a very general version of this preservationist approach to paraconsistency.