Neighborhoods for Entailment

This paper presents a neighborhood semantics for logics of entailment. It begins with a minimal system Min that expresses the most fundamental assumptions about the entailment relation, and continues by examining various extensions that reflect further assumptions that might be made about entailment. This leads first to the logic B that is the basic relevant logic, and then to more powerful systems. All of these logics are proved to be sound and strongly complete. With B the neighborhood semantics meets the Routley–Meyer relational semantics for relevant logic; these connections are examined. The minimal and basic entailment logics are shown to have the finite model property, and hence to be decidable.     

Duality and Canonical Extensions of Bounded Distributive Lattices with Operators,and Applications to the Semantics of Non-Classical Logics II

The main goal of this paper is to explain the link between the algebraic models and the Kripke-style models for certain classes of propositional non-classical logics. We consider logics that are sound and complete with respect to varieties of distributive lattices with certain classes of well-behaved operators for which a Priestley-style duality holds, and present a way of constructing topological and non-topological Kripke-style models for these types of logics. Moreover, we show that, under certain additional assumptions on the variety of the algerabic models of the given logics, soundness and completeness with respect to these classes of Kripke-style models follows by using entirely algebraical arguments from the soundness and completeness of the logic with respect to its algebraic models.     

Making Things Happen

We explore some logics of change, focusing on commands to change the world in such a way that certain elementary propositions become true or false. This investigation starts out from the following two simplifying assumptions: (1) the world is a collection of facts (Wittgenstein), and (2), the world can be changed by changing elementary facts (Marx). These assumptions allow us to study the logic of imperatives in the simplest possible setting.     

Probabilistic reasoning in a classical logic

We offer a view on how probability is related to logic. Specifically, we argue against the widely held belief that standard classical logics have no direct way of modelling the certainty of assumptions in theories and no direct way of stating the certainty of theorems proved from these (uncertain) assumptions. The argument rests on the observation that probability densities, being functions, can be represented and reasoned with naturally and directly in (classical) higher-order logic.     

Probabilistic argumentation systems: A new way to combine logic with probability

Probability is usually closely related to Boolean structures, i.e., Boolean algebras or propositional logic. Here we show, how probability can be combined with non-Boolean structures, and in particular non-Boolean logics. The basic idea is to describe uncertainty by (Boolean) assumptions, which may or may not be valid. The uncertain information depends then on these uncertain assumptions, scenarios or interpretations. We propose to describe information in information systems, as introduced by Scott into domain theory. This captures a wide range of systems of practical importance such as many propositional logics, first order logic, systems of linear equations, inequalities, etc. It covers thus both symbolic as well as numerical systems. Assumption-based reasoning allows then to deduce supporting arguments for hypotheses. A probability structure imposed on the assumptions permits to quantify the reliability of these supporting arguments and thus to introduce degrees of support for hypotheses. Information systems and related information algebras are formally introduced and studied in this paper as the basic structures for assumption-based reasoning. The probability structure is then formally represented by random variables with values in information algebras. Since these are in general non-Boolean structures some care must be exercised in order to introduce these random variables. It is shown that this theory leads to an extension of Dempster–Shafer theory of evidence and that information algebras provide in fact a natural frame for this theory.     

Representation of Muslim sexual subjectivities: the hidden ethical judgments of journalistic rhetoric

In 2005, following a year of increased attention in English language media to the prominence of sexual reassignment surgeries in Iran, the London-based Guardian dubs Tehran “the unlikely sex-change capital of the world.” This title is significantly complicated when we realize that according to mainstream English media, Tehran is not the first or only sex change capital of the world. Its sister city is Trinidad, Colorado, a predominantly Catholic town with a population hovering around 9,000. Although English language newspapers have served up stories of each location as “surprising” magnets for SRS, none have mentioned both places in the same article because these stories operate with a different set of logics related to religion, sex, and human rights. Analysis of the journalist rhetoric of these two unlikely capitals highlights these diverse logics, particularly how assumptions about Muslim subjectivity affects judgments about the status of sexual freedom in Iran.     

Substructural logics,pluralism and collapse

When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in a clear sense, non-identical to it. We argue that this phenomenon can be generalized, given the existence of logics which coincide with Classical Logic regarding a number of metainferential levels—although they are, again, clearly different systems. We claim this highlights the need to arrive at a more refined version of the Collapse Argument, which we discuss at the end of the paper.

     

Conditionals,probability, and non-triviality

We show that the implicational fragment of intuitionism is the weakest logic with a non-trivial probabilistic semantics which satisfies the thesis that the probabilities of conditionals are conditional probabilities. We also show that several logics between intuitionism and classical logic also admit non-trivial probability functions which satisfy that thesis. On the other hand, we also prove that very weak assumptions concerning negation added to the core probability conditions with the restriction that probabilities of conditionals are conditional probabilities are sufficient to trivialize the semantics.     

Simulation and Transfer Results in Modal Logic – A Survey

This papers gives a survey of recent results about simulations of one class of modal logics by another class and of the transfer of properties of modal logics under extensions of the underlying modal language. We discuss: the transfer from normal polymodal logics to their fusions, the transfer from normal modal logics to their extensions by adding the universal modality, and the transfer from normal monomodal logics to minimal tense extensions. Likewise, we discuss simulations of normal polymodal logics by normal monomodal logics, of nominals and the difference operator by normal operators, of monotonic monomodal logics by normal bimodal logics, of polyadic normal modal logics by polymodal normal modal logics, and of intuitionistic modal logics by normal bimodal logics.     

Neoliberal ideology in work and organizational psychology

This paper explores the role of neoliberal ideology in workplace practices and in work and organizational psychology (WOP) research. It analyses how neoliberal ideology manifests in these two domains by using a prominent framework from the field of political theory to understand ideology through three different logics: political, social and fantasmatic logics. We explore the main neoliberal assumptions underlying existing practices in the workplace as well as in WOP research, how individuals are gripped by such practices, and how the status quo is maintained. The paper analyses how individuals in the contemporary workplace are henceforth influenced by neoliberalism, and how this is reflected in the practices and dominant paradigms within WOP. In particular, we focus on three ways neoliberalism affects workplaces and individual experiences of the workplace: through instrumentality, individualism and competition. The paper finishes with practical recommendations for researchers and practitioners alike on how to devote more attention to the, often implicit, role of neoliberal ideology in their work and research. The discussion elaborates on how alternative paradigms in the workplace can be developed which address the downsides of neoliberalism.     

On maximal intermediate predicate constructive logics

We extend to the predicate frame a previous characterization of the maximal intermediate propositional constructive logics. This provides a technique to get maximal intermediate predicate constructive logics starting from suitable sets of classically valid predicate formulae we call maximal nonstandard predicate constructive logics. As an example of this technique, we exhibit two maximal intermediate predicate constructive logics, yet leaving open the problem of stating whether the two logics are distinct. Further properties of these logics will be also investigated.Presented by H. Ono     

Modal translations in substructural logics

Substructural logics are logics obtained from a sequent formulation of intuitionistic or classical logic by rejecting some structural rules. The substructural logics considered here are linear logic, relevant logic and BCK logic. It is proved that first-order variants of these logics with an intuitionistic negation can be embedded by modal translations into S40type extensions of these logics with a classical, involutive, negation. Related embeddings via translations like the double-negation translation are also considered. Embeddings into analogues of S4 are obtained with the help of cut climination for sequent formulations of our substructural logics and their modal extensions. These results are proved for systems with equality too.     

Characterizing Equivalential and Algebraizable Logics by the Leibniz Operator

In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz operator. Thus, from a characterization of equivalential logics we obtain a new short proof of the main result of [2] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics. We characterize equivalential and, by adding injectivity, p.i.-algebraizable logics.     

Adaptive Logic Characterizations of Input/Output Logic

We translate unconstrained and constrained input/output logics as introduced by Makinson and van der Torre to modal logics, using adaptive logics for the constrained case. The resulting reformulation has some additional benefits. First, we obtain a proof-theoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our framework naturally gives rise to useful variants and allows to express important notions that go beyond the expressive means of input/output logics, such as violations and sanctions.     

An algebraic approach to intuitionistic modal logics in connection with intermediate predicate logics

Modal counterparts of intermediate predicate logics will be studied by means of algebraic devise. Our main tool will be a construction of algebraic semantics for modal logics from algebraic frames for predicate logics. Uncountably many examples of modal counterparts of intermediate predicate logics will be given. Dedicated to Prof. T. Umezawa on his 60th birthday     

Kripke bundles for intermediate predicate logics and Kripke frames for intuitionistic modal logics

Shehtman and Skvortsov introduced Kripke bundles as semantics of non-classical first-order predicate logics. We show the structural equivalence between Kripke bundles for intermediate predicate logics and Kripke-type frames for intuitionistic modal prepositional logics. This equivalence enables us to develop the semantical study of relations between intermediate predicate logics and intuitionistic modal propositional logics. New examples of modal counterparts of intermediate predicate logics are given.The author would like to express his gratitude to Professor Hiroakira Ono for his comments, and to Professor Tadashi Kuroda for his encouragement.The author wishes to express his gratitude to Professors V. B. Shehtman, D. P. Skvortsov and M. Takano for their comments.     

A Hierarchy of Weak Double Negations

In this paper, a way of constructing many-valued paraconsistent logics with weak double negation axioms is proposed. A hierarchy of weak double negation axioms is addressed in this way. The many-valued paraconsistent logics constructed are defined as Gentzen-type sequent calculi. The completeness and cut-elimination theorems for these logics are proved in a uniform way. The logics constructed are also shown to be decidable.     

Displaying and Deciding Substructural Logics 1: Logics with Contraposition

Many logics in the relevant family can be given a proof theory in the style of Belnap's display logic (Belnap, 1982). However, as originally given, the proof theory is essentially more expressive than the logics they seek to model. In this paper, we consider a modified proof theory which more closely models relevant logics. In addition, we use this proof theory to show decidability for a large range of substructural logics.