A propositional logic of explicit proofs, LP, was introduced in [S. Artemov, Explicit provability and constructive semantics, The Bulletin for Symbolic Logic 7 1–36], completing a project begun long ago by Gödel, [K. Gödel, Vortrag bei Zilsel, translated as Lecture at Zilsel’s in: S. Feferman , Kurt Gödel Collected Works III, 1938, pp. 62–113]. In fact, LP can be looked at in a more general way, as a logic of explicit evidence, and there have been several papers along these (...) lines. A major result about LP is the Realization Theorem, that says any theorem of S4 can be converted into a theorem of LP by some replacement of necessitation symbols with explicit proof terms. Thus the necessitation operator of S4 can be seen as a kind of implicit existential quantifier: there exists a proof term such that…. In this paper, quantification over evidence is introduced into LP, and it is shown that the connection between S4 necessitation and the existential quantifier becomes an explicit one. The extension of LP with quantifiers is called QLP. A semantics and an axiom system for QLP are given, soundness and completeness are established, and several results are proved relating QLP to LP and to S4. (shrink)

Three variants of Kurt Gödel's ontological argument, proposed by Dana Scott, C. Anthony Anderson and Melvin Fitting, are encoded and rigorously assessed on the computer. In contrast to Scott's version of Gödel's argument the two variants contributed by Anderson and Fitting avoid modal collapse. Although they appear quite different on a cursory reading they are in fact closely related. This has been revealed in the computer-supported formal analysis presented in this article. Key to our formal analysis is the (...) utilization of suitably adapted notions of ultrafilters, and a careful distinction between extensions and intensions of positive properties. (shrink)

We argue that we can avoid epistemic dilemmas by properly understanding the nature and epistemology of the suspension of judgment, with a particular focus on conflicts between higher-order evidence and first-order evidence.

We argue for a novel view of suspending judgment properly--i.e., suspending judgment in an ex post justified way. In so doing we argue for a Kantian virtue-theoretic view of epistemic normativity and against teleological virtue-theoretic accounts.

This research examines the relationships between education in business ethics, Reynolds’s (J Appl Psychol 93:1027–1041, 2008) “moral attentiveness” construct, or the extent to which individuals chronically perceive and reflect on morality and moral elements in their experiences, and Singhapakdi et al.’s (J Bus Ethics 15:1131–1140, 1996) measure of perceptions of the role of ethics and social responsibility (PRESOR). Education in business ethics was found to be positively associated with the two identified factors of moral attentiveness, “reflective” and “perceptual” moral attentiveness, (...) and with the PRESOR “stakeholder view” factor. Also, reflective moral attentiveness was found to act as a mediator in the relationship between education in business ethics and the PRESOR stakeholder view factor. Evidence of gender and social desirability bias effects was also found. The implications of these relationships and social cognitive theory for improved understanding of the mechanisms by which a variety of variables have their effects on PRESOR in business are discussed. (shrink)

There is an obvious difference between what a term designates and what it means. At least it is obvious that there is a difference. In some way, meaning determines designation, but is not synonymous with it. After all, “the morning star” and “the evening star” both designate the planet Venus, but don't have the same meaning. Intensional logic attempts to study both designation and meaning and investigate the relationships between them.

Strict/tolerant logic, ST, evaluates the premises and the consequences of its consequence relation differently, with the premises held to stricter standards while consequences are treated more tolerantly. More specifically, ST is a three-valued logic with left sides of sequents understood as if in Kleene’s Strong Three Valued Logic, and right sides as if in Priest’s Logic of Paradox. Surprisingly, this hybrid validates the same sequents that classical logic does. A version of this result has been extended to meta, metameta, … (...) consequence levels in Barrio et al.. In my earlier paper Fitting I showed that the original ideas behind ST are, in fact, much more general than first appeared, and an infinite family of many valued logics have Strict/Tolerant counterparts. This family includes both Kleene’s and Priest’s logic individually, as well as first degree entailment. For instance, for both the Kleene and the Priest logic, the corresponding strict/tolerant logic is six-valued, but with differing sets of strictly and tolerantly designated truth values. The present paper extends that generalization in two directions. We examine a reverse notion, of Tolerant/Strict logics, which exist for the same structures that were investigated in Fitting. And we show that the generalization extends through the meta, metameta, … consequence levels for the same infinite family of many valued logics. Finally we close with remarks on the status of cut and related rules, which can actually be rather nuanced. Throughout, the aim is not the philosophical applications of the Strict/Tolerant idea, but the determination of how general a phenomenon it is. (shrink)

Nested sequent systems for modal logics are a relatively recent development, within the general area known as deep reasoning. The idea of deep reasoning is to create systems within which one operates at lower levels in formulas than just those involving the main connective or operator. Prefixed tableaus go back to 1972, and are modal tableau systems with extra machinery to represent accessibility in a purely syntactic way. We show that modal nested sequents and prefixed modal tableaus are notational variants (...) of each other, roughly in the same way that tableaus and Gentzen sequent calculi are notational variants. This immediately gives rise to new modal nested sequent systems which may be of independent interest. We discuss some of these, including those for some justification logics that include standard modal operators. (shrink)

Several justification logics have been created, starting with the logic LP, [1]. These can be thought of as explicit versions of modal logics, or of logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. We begin by sketching the basics of justification logics and their relations with modal logics. Then we move to new material. Modal logics come in various strengths. For their corresponding justification logics, differing (...) strength is reflected in different vocabularies. What we show here is that for justification logics corresponding to modal logics extending T, various familiar extensions are actually conservative with respect to each other. Our method of proof is very simple, and general enough to handle several justification logics not directly corresponding to distinct modal logics. Our methods do not, however, allow us to prove comparable results for justification logics corresponding to modal logics that do not extend T. That is, we are able to handle explicit logics of knowledge, but not explicit logics of belief. This remains open. (shrink)

In the tech report Artemov and Yavorskaya [4] an elegant formulation of the first-order logic of proofs was given, FOLP. This logic plays a fundamental role in providing an arithmetic semantics for first-order intuitionistic logic, as was shown. In particular, the tech report proved an arithmetic completeness theorem, and a realization theorem for FOLP. In this paper we provide a possible-world semantics for FOLP, based on the propositional semantics of Fitting [5]. We also give an Mkrtychev semantics. Motivation and intuition (...) for FOLP can be found in Artemov and Yavorskaya [4], and are not fully discussed here.This paper is dedicated to Sergei Artemov, an honored colleague and friend, who has made wonderful things for the rest of us to play with. (shrink)

LP can be seen as a logic of knowledge with justifications. See [S. Artemov, The logic of justification, The Review of Symbolic Logic 1 477–513] for a recent comprehensive survey of justification logics generally. Artemov’s Realization Theorem says justifications can be extracted from validities in the more conventional Hintikka-style logic of knowledge S4, in which they are not explicitly present. Justifications, however, are far from unique. There are many ways of realizing each theorem of S4 in the logic LP. If (...) the machinery of justifications is to be applied to artificial intelligence, or better yet, to everyday reasoning, we will need to work with whatever justifications we may have at hand—one version may not be interchangeable with another, even though they realize the same S4 formula. In this paper we begin the process of providing tools for reasoning about justifications directly. The tools are somewhat complex, but in retrospect this should not be surprising. Among other things, we provide machinery for combining two realizations of the same formula, and for replacing subformulas by equivalent subformulas. The results are algorithmic in nature—semantics for LP plays no role. We apply our results to provide a new algorithmic proof of Artemov’s Realization Theorem itself. This paper is a much extended version of [M.C. Fitting, Realizations and LP, in: S. Artemov, A. Nerode , Logical Foundations of Computer Science—New York ’07, in: Lecture Notes in Computer Science, vol. 4514, Springer-Verlag, 2007, pp. 212–223]. (shrink)

Der klassische subjekt- und handlungsbezogene Machtbegriff ist ungeeignet, sowohl die sozialen Prozesse der Gesellschaften der Postmoderne, als auch speziell der Wirtschaft verständlich zu machen. Im Sinne einer Sozialphilosophie des kommunikativen Textes, d. h. eines Zwischen, einer Medialität, ist vielmehr ein Begriff der Macht zu entwickeln, der diese als modale Relation entwirft. Modale Relationen konturieren Möglichkeitsräume, die die Gestalt mehrdimensionaler Netze haben. Im ökonomischen Extremphänomen der globalisierten Finanzökonomie haben diese Netze ihre deutlichste Gestalt der Ablösung der Macht in den Netzen von (...) jeder Subjektivität. Insofern sind diese ökonomischen Netze das eigentliche Signum der Postmoderne. (shrink)

Name der Zeitschrift: Neue Zeitschrift für Systematische Theologie und Religionsphilosophie Jahrgang: 58 Heft: 2 Seiten: 129-148.

In an earlier paper, [5], I gave semantics and tableau rules for a simple firstorder intensional logic called FOIL, in which both objects and intensions are explicitly present and can be quantified over. Intensions, being non-rigid, are represented in FOIL as (partial) functions from states to objects. Scoping machinery, predicate abstraction, is present to disambiguate sentences like that asserting the necessary identity of the morning and the evening star, which is true in one sense and not true in another.In this (...) paper I address the problem of axiomatizing FOIL. I begin with an interesting sublogic with predicate abstraction and equality but no quantifiers. In [2] this sublogic was shown to be undecidable if the underlying modal logic was at least K4, though it is decidable in other cases. The axiomatization given is shown to be complete for standard logics without a symmetry condition. The general situation is not known. After this an axiomatization for the full FOIL is given, which is straightforward after one makes a change in the point of view. (shrink)

Until quite recently, the virtually unchallenged position of those scientists who studied the way people acquire their morality was cultural and ethical relativism. The central tenet of that position is this: although all societies have a morality, that is, a set of general authoritative norms and standards to which its members are expected if not compelled to conform, these norms and standards not only vary enormously from one society to another, but there is no objective way of ranking them. In (...) particular, there is no single ideal objective moral order, to which these various social moralities can be seen as less or more successful approximations, and which enables us to appraise them, on the basis of the degree of that approximation, as less or more advanced, sound, or valid. The whole of morality is thus construed as “agent-morality”: a measure of a person’s concern to conform his behavior to “objective” norms and standards; on the relativist view those dominant in the group to which he belongs. On this view, the role of moral education would be confined to assisting and making more efficient the informal processes by which the current moral norms and standards of the group become internalized in its members. Socialization is conceived as a purely one-way process: that of moulding the individual so that he will conform to the group mores. (shrink)

Bd. 1. Wertphilosophie und Ethik -- Bd. 2. Bathik und Ästhetik -- Bd. 3. Kulturphilosophie, Gesellschafts- und Staatslehre -- Bd. 4. Erkenntnistheorie und Ontologie -- Bd. 6. Die Enge des Bewusstseins.

Hybrid logics internalize their own semantics. Members of the newer family of justification logics internalize their own proof methodology. It is an appealing goal to combine these two ideas into a single system, and in this paper we make a start. We present a hybrid/justification version of the modal logic T. We give a semantics, a proof theory, and prove a completeness theorem. In addition, we prove a Realization Theorem, something that plays a central role for justification logics generally. Since (...) justification logics are newer and less well-known than hybrid logics, we sketch their background, and give pointers to their range of applicability. We conclude with suggestions for future research. Indeed, the main goal of this paper is to encourage others to continue the investigation begun here. (shrink)

This book describes computability theory and provides an extensive treatment of data structures and program correctness. It makes accessible some of the author's work on generalized recursion theory, particularly the material on the logic programming language PROLOG, which is currently of great interest. Fitting considers the relation of PROLOG logic programming to the LISP type of language.