Theories about the ontological structure of the world have generally been described in informal, intuitive terms. This book offers an account of the general features and methodology of formal ontology. The book defends conceptual realism as the best system to adopt based on a logic of natural kinds. By formally reconstructing an intuitive, informal ontological scheme as a formal ontology we can better determine the consistency and adequacy of that scheme.

We shall describe the set of strongly meet irreducible logics in the lattice ϵLin.t of normal tense logics of weak orderings. Based on this description it is shown that all logics in ϵLin.t are independently axiomatizable. Then the description is used in order to investigate tense logics with respect to decidability, finite axiomatizability, axiomatization problems and completeness with respect to Kripke semantics. The main tool for the investigation is a translation of bimodal formulas into a language talking about partitions of (...) general frames into intervals so that relative to both Kripke frames and descriptive frames the expressive power of both languages coincides. (shrink)

The proof of the Second Incompleteness Theorem consists essentially of proving the uniqueness and explicit definability of the sentence asserting its own unprovability. This turns out to be a rather general phenomenon: Every instance of self-reference describable in the modal logic of the standard proof predicate obeys a similar uniqueness and explicit definability law. The efficient determination of the explicit definitions of formulae satisfying a given instance of self-reference reduces to a simple algebraic problem-that of solving the corresponding fixed-point equation (...) in the modal logic. We survey techniques for the efficient calculation of such fixed-points. (shrink)

The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a ‘quantified’ part, a temporal part, a modal (alethic) part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of$$T \times W$$T×Wmodels, and the (...) proof-theoretical apparatus of semantic tableaux. The ‘quantified part’ of the systems includes relational predicates and the identity symbol. The quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The tableaux rules are classical. The alethic part contains two types of modal operators for absolute and historical necessity and possibility. According to ‘boulesic logic’ (the logic of the will), ‘willing’ (‘consenting’, ‘rejecting’, ‘indifference’ and ‘non-indifference’) is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats ‘believing’ (and ‘conceiving’) as a kind of modal operator. I will explore some possible relationships between these different parts, and investigate some principles that include more than one type of logical expression. I will show that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider an example of a valid argument and an example of an invalid sentence. I show how one can use semantic tableaux to establish validity and invalidity and read off countermodels. These examples illustrate the philosophical usefulness of the systems that are introduced in this paper. (shrink)

In this paper, I will develop a set of boulesic-doxastic tableau systems and prove that they are sound and complete. Boulesic-doxastic logic consists of two main parts: a boulesic part and a doxastic part. By ‘boulesic logic’ I mean ‘the logic of the will’, and by ‘doxastic logic’ I mean ‘the logic of belief’. The first part deals with ‘boulesic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be (...) the case that’ and ‘individual x accepts that it is the case that’. The second part deals with ‘doxastic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of doxastic expression: ‘individual x believes that’ and ‘it is imaginable to individual x that’. Boulesic-doxastic logic investigates how these concepts are related to each other. Boulesic logic is a new kind of logic. Doxastic logic has been around for a while, but the approach to this branch of logic in this paper is new. Each system is combined with modal logic with two kinds of modal operators for historical and absolute necessity and predicate logic with necessary identity and ‘possibilist’ quantifiers. I use a kind of possible world semantics to describe the systems semantically. I also sketch out how our basic language can be extended with propositional quantifiers. All the systems developed in this paper are new. (shrink)

Arthur N. Prior, in the Preface of Past, Present and Future, made clear his indebtedness to “the very lively tense-logicians of California for many discussions”. Strangely,with a notable exception of Copeland, there is no extensive discussion of these scholars in the literature on the history of tense logic. In this paper, I propose to study how Nino B. Cocchiarella, as one of the Californian tense-logicians, interacted with Prior in the late 1960s. By gathering clues from their correspondence available at Virtual (...) Lab for Prior Studies, I will highlight some of the differences between their views on tense-logic, which might still have far-reaching philosophical implications. I will conclude with a sketchof how to study in what ways Prior and Cocchiarella influenced some other Californian tense-logicians. (shrink)

Algebraic approach to study of classical and non-classical logical calculi was developed and systematically presented by Helena Rasiowa in [48], [47]. It is very fruitful in investigation of non-classical logics because it makes possible to study large families of logics in an uniform way. In such research one can replace logics with suitable classes of algebras and apply powerful machinery of universal algebra. In this paper we present an overview of results on interpolation and definability in modal and positive logics,and (...) also in extensions of Johansson's minimal logic. All these logics are strongly complete under algebraic semantics. It allows to combine syntactic methods with studying varieties of algebras and to flnd algebraic equivalents for interpolation and related properties. Moreover, we give exhaustive solution to interpolation and some related problems for many families of propositional logics and calculi. (shrink)

We propose a first order modal logic, theQS4E-logic, obtained by adding to the well-known first order modal logicQS4 arigidity axiom schemas:A → □A, whereA denotes a basic formula. In this logic, thepossibility entails the possibility of extending a given classical first order model. This allows us to express some important concepts of classical model theory, such as existential completeness and the state of being infinitely generic, that are not expressibile in classical first order logic. Since they can be expressed in (...) -logic, we are also induced to compare the expressive powers ofQS4E and . Some questions concerning the power of rigidity axiom are also examined. (shrink)

Recent theories of agency (sees to it that) of Nuel Belnap and Michael Perloff are examined, particularly in the context of an early proposal of the author.

This paper offers a semantic study in multi-relational semantics of quantified N-Monotonic modal logics with varying domains with and without the identity symbol. We identify conditions on frames to characterise Barcan and Ghilardi schemata and present some related completeness results. The characterisation of Barcan schemata in multi-relational frames with varying domains shows the independence of BF and CBF from well-known propositional modal schemata, an independence that does not hold with constant domains. This fact was firstly suggested for classical modal systems (...) by Stolpe, 557–575, 2003), but unfortunately that work used only models and not frames. (shrink)

The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer in the first part of the paper a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like (...) FOL + K)in terms of neighborhood frames with constant domains. The first order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. Models of this type are either difficult of impossible to build in terms of relational Kripkean semantics [40].We conclude by introducing general first order neighborhood frames with constant domains and we offer a general completeness result for the entire family of classical first order modal systems in terms of them, circumventing some well-known problems of propositional and first order neighborhood semantics (mainly the fact that many classical modal logics are incomplete with respect to an unmodified version of either neighborhood or relational frames). We argue that the semantical program that thus arises offers the first complete semantic unification of the family of classical first order modal logics. (shrink)

I proffer a success argument for classical logical consequence. I articulate in what sense that notion of consequence should be regarded as the privileged notion for metaphysical inquiry aimed at uncovering the fundamental nature of the world. Classical logic breeds necessitism. I use necessitism to produce problems for both ontological naturalism and atheism.

The system R, or more precisely the pure implicational fragment R›, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance logic is RM or R-mingle. The question is whether adding mingle axiom to R› yields the pure implicational fragment RM› of the system? As concerns the weak systems there are at least two (...) approaches to the problem. First of all, it is possible to restrict a validity of some theorems. In another approach we can investigate even weaker logics which have no theorems and are characterized only by rules of deducibility. (shrink)