Complex Predicates and Logics for Properties and Relations

According to an influential tradition, a predicate of one's preferred theory ought to correspond to something in the world, a feature shared by the various entities that satisfy the predicate. 1 If the predicate 'is a kangaroo' occurs in one's preferred theory, then one ought to posit a property which all of the various things that satisfy 'is a kangaroo' have in common. 2 Philosophers of this persuasion divide into two camps. Some endorse sparse conceptions of properties on which some collections of entities lack a common property. Therefore, they hesitate to deploy additional predicates in their preferred description of the world. The predicates of day-to-day language or special sciences likely do not correspond to properties. These predicates then must ultimately give way to the predicates of a more austere schema. Other property theorists endorse abundant conceptions: every arbitrary grouping of individuals shares some property. A theory would be no worse for having a predicate corresponding to any such grouping.

2016

This paper presents an account of what it is for a property or relation (or ‘attribute’ for short) to be logically simple. Based on this account, it is shown, among other things, that the logically simple attributes are in at least one important way sparse. This in turn lends support to the view that the concept of a logically simple attribute can be regarded as a promising substitute for Lewis’s concept of a perfectly natural attribute. At least in part, the advantage of using the former concept lies in the fact that it is amenable to analysis, where that analysis—i.e., the account put forward in this paper—requires the adoption neither of an Armstrongian theory of universals nor of a primitive notion of naturalness, fundamentality, or grounding.

Journal of Philosophical Logic

Knowledge Engineering and Knowledge …, 2000

2022

A Universal Mapping Property is generally described as a characterization of an object up to a unique isomorphism by considering its relation to every other object; however, the term "by considering its relation to every other object" is not clearly or explicitly defined. In this paper, we will introduce such definition which will also generalize the idea of a universal property from a logical perspective.

2012

We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and complete- ness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems.

2019

The history of philosophy is rich with theories about objects; theories of object kinds, their nature, the status of their existence, etc. In recent years philosophical logicians have attempted to formalize some of these theories, yielding many fruitful results. This thesis intends to add to this tradition in philosophical logic by developing a second-order formal system that may serve as a groundwork for a multitude of theories of objects (e.g. concrete and abstract objects, impossible objects, fictional objects, and others). Through the addition of what we may call sortal quantifiers (i.e. quantifiers that bind individual variables ranging over objects of three unique sorts), a groundwork for a logic that captures concrete and non-concrete objects will be developed. We then extend this groundwork by the addition of a single new operator and the modal operators of a Priorian temporal logic. From this extension, our formal system can represent and define concrete, abstract, fictional, and impossible objects as well as formally axiomatize informal theories of them.

Proceedings of the fifth conference on European chapter of the Association for Computational Linguistics -, 1991

This paper describes a classical logic for attribute-value (or feature description) languages which ate used in urfification grammar to describe a certain kind of linguistic object commonly called attribute-value structure (or feature structure). Tile algorithm which is used for deciding satisfiability of a feature description is based on a restricted deductive closure construction for sets of literals (atomic formulas and negated atomic formulas). In contrast to the Kasper/Rounds approach (cf. [Kasper/Rounds 90]), we can handle cyclicity, without the need for the introduction of complexity norms, as in [Johnson 88J and [Beierle/Pletat 88]. The deductive closure construction is the direct proof-theoretic correlate of the congruence closure algorithm (cf. [Nelson/Oppen 80]), if it were used in attributevalue languages for testing satisfiability of finite sets of literals.

2015

Bergamo’s conference on the metaphysics of properties and relations was one of the most attractive conferences that recently took place in Italy. When we first looked at the program some nine months ago, few things if anything could have contained our enthusiasm: Not only did it confirm that properties and relations keep exerting large interest at all levels of the discipline, but it brought together some among the most reputed scholars and promised to bring about novel issues as well as thought-provoking proposals. We immediately set up a team of RIFAJ-editors whose competences could have most nearly approximate the covered topics. Ilaria Canavotto considered Kevin Mulligan’s defence of the thesis that connectives are more fundamental than predicates and his attempt to make a weak and a strong form of realism about the semantic value of connectives (which he calls ‘connectors’) compatible. She also outlined Fabrice Correia’s proposal of exploiting the notion of generic identity in ...

Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1988