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].     

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.     

The Logic of Instance Ontology

An ontology's theory of ontic predication has implications for the concomitant predicate logic. Remarkable in its analytic power for both ontology and logic is the here developed Particularized Predicate Logic (PPL), the logic inherent in the realist version of the doctrine of unit or individuated predicates. PPL, as axiomatized and proven consistent below, is a three-sorted impredicative intensional logic with identity, having variables ranging over individuals x, intensions R, and instances of intensions Ri. The power of PPL is illustrated by its clarification of the self-referential nature of impredicative definitions and its distinguishing between legitimate and illegitimate forms. With a well-motivated refinement on the axiom of comprehension, PPL is, in effect, a higher-order logic without a forced stratification of predicates into types or the use of other ad hoc restrictions. The Russell–Priest characterization of the classic self-referential paradoxes is used to show how PPL diagnosis and solves these antimonies. A direct application of PPL is made to Grelling's Paradox. Also shown is how PPL can distinguish between identity and indiscernibility.     

Absolute Probability Functions for Intuitionistic Propositional Logic

Provided here is a characterisation of absolute probability functions for intuitionistic (propositional) logic L, i.e. a set of constraints on the unary functions P from the statements of L to the reals, which insures that (i) if a statement A of L is provable in L, then P(A) = 1 for every P, L's axiomatisation being thus sound in the probabilistic sense, and (ii) if P(A) = 1 for every P, then A is provable in L, L's axiomatisation being thus complete in the probabilistic sense. As there are theorems of classical (propositional) logic that are not intuitionistic ones, there are unary probability functions for intuitionistic logic that are not classical ones. Provided here because of this is a means of singling out the classical probability functions from among the intuitionistic ones.     

The Relation between Formal and Informal Logic

The issue of the relationship between formal and informal logic depends strongly on how one understands these two designations. While there is very little disagreement about the nature of formal logic, the same is not true regarding informal logic, which is understood in various (often incompatible) ways by various thinkers. After reviewing some of the more prominent conceptions of informal logic, I will present my own, defend it and then show how informal logic, so understood, is complementary to formal logic.