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Formal Ontology and Logical Syntax

E. J. Lowe

in The Four-Category Ontology: A Metaphysical Foundation for Natural Science

Published in print:
2005
Published Online:
May 2006
ISBN:
9780199254392
eISBN:
9780191603600
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199254397.003.0004
Subject:
Philosophy, Metaphysics/Epistemology

Traditional formal logic as developed by Fred Sommers is compared and contrasted with the modern quantified predicate logic that we owe to Gottlob Frege and Bertrand Russell; the latter is argued to ... More


INTERPOLATION AND DEFINABILITY IN QUANTIFIED LOGICS

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter contains a proof of Lyndon's interpolation property (LIP) for quantified extensions of basic modal logics K, T, D, K4, and S4, and for some others, including the propositional S5 has ... More


THE INTERPOLATION THEOREM IN INTUITIONISTIC PREDICATE CALCULUS

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0004
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter presents the equivalence of Craig's interpolation property to Robinson's joint consistency, and a proof of Lyndon's interpolation theorem for the classical predicate logic. It is proved ... More


Second-Order Modal Logic

Nino B. Cocchiarella and Max A. Freund

in Modal Logic: An Introduction to its Syntax and Semantics

Published in print:
2008
Published Online:
October 2011
ISBN:
9780195366587
eISBN:
9780199851898
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195366587.003.0009
Subject:
Philosophy, Philosophy of Language

This chapter extends the systems to the level of second-order modal predicate logic, where the notion of existence that is central to the actualism-possibilism distinction is given deeper and ... More


INTERPOLATION IN (INTUITIONISTIC) LOGIC PROGRAMMING

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0015
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter provides interpolation results for the Horn clause fragment of classical or intuitionistic logic. A weak variant of interpolation for a fragment of the intuitionistic predicate logic ... More


Logical power, Abelard, and empirical success rates

Pieter A. M. Seuren

in The Logic of Language: Language From Within Volume II

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199559480
eISBN:
9780191721144
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199559480.003.0004
Subject:
Linguistics, Semantics and Pragmatics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics

Aristotle's predicate logic does not suffer from undue existential import (UEI). Abelard followed Aristotle in this respect. The notion of logical power is defined and it is shown that the Square has ... More


The Semantics of Classical Predicate Logic

Charles S. Chihara

in The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic

Published in print:
2001
Published Online:
October 2011
ISBN:
9780199246557
eISBN:
9780191697609
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199246557.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

One striking feature of both Graeme Forbes and Gideon Rosen's anti-realism is the absence of any analysis of the role that possible worlds interpretations or structures play in modal logic. To avoid ... More


Predicates and Quantifiers

Mark Schroeder

in Being For: Evaluating the Semantic Program of Expressivism

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199534654
eISBN:
9780191715938
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534654.003.0006
Subject:
Philosophy, Philosophy of Language

This chapter shows how to expand the ideas of Chapter 5 for a language involving quantifiers, and offers a more rigorous treatment. Since the contents of states of being for are treated as ... More


Quantified Modal Logic

Nino B. Cocchiarella and Max A. Freund

in Modal Logic: An Introduction to its Syntax and Semantics

Published in print:
2008
Published Online:
October 2011
ISBN:
9780195366587
eISBN:
9780199851898
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195366587.003.0007
Subject:
Philosophy, Philosophy of Language

This chapter describes the syntax of first-order modal predicate logic and develops the first-order extensions of the different sentential modal logics constructed in Chapter 2. The authors ... More


Classical Logic

JC Beall

in Logical Pluralism

Published in print:
2005
Published Online:
October 2011
ISBN:
9780199288403
eISBN:
9780191700491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199288403.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

Logical pluralism addresses the following conditions. First, the settled core of consequence is given in the Generalised Tarski Thesis (GTT). Second, an instance of GTT is obtained by a specification ... More


Predicate Languages

Jon Williamson

in In Defence of Objective Bayesianism

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199228003
eISBN:
9780191711060
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228003.003.0005
Subject:
Mathematics, Probability / Statistics, Logic / Computer Science / Mathematical Philosophy

Thus far we have considered objective Bayesian probability to be defined over finite propositional languages. This chapter extends the formalism to predicate languages. As well as reaping the rewards ... More


The Semantics of Quantified Modal Logic

Nino B. Cocchiarella and Max A. Freund

in Modal Logic: An Introduction to its Syntax and Semantics

Published in print:
2008
Published Online:
October 2011
ISBN:
9780195366587
eISBN:
9780199851898
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195366587.003.0008
Subject:
Philosophy, Philosophy of Language

The authors develop semantics for first-order modal predicate logic in terms of standard model theory, the models of which we take to be set-theoretic counterparts of possible worlds. A primary ... More


The Logic of Language: Language From Within Volume II

Pieter A. M. Seuren

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199559480
eISBN:
9780191721144
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199559480.001.0001
Subject:
Linguistics, Semantics and Pragmatics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics

The Logic of Language opens a new perspective on logic. Seuren first argues that the logic of language derives from the lexical meanings of the logical operators. These meanings, ... More


Miscellaneous Strategies

John P. Burgess and Gideon Rosen

in A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198250128
eISBN:
9780191597138
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198250126.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics

Indicates very briefly a variety of further strategies, beginning with modifications and combinations of the three that were discussed in the preceding three chapters. The more exotic strategies are ... More


Logical Entailment

Jon Williamson

in Lectures on Inductive Logic

Published in print:
2017
Published Online:
March 2017
ISBN:
9780199666478
eISBN:
9780191749292
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199666478.003.0006
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

Chapter 6 explains how objective Bayesian inductive logic captures logical entailment. This is essentially because the logic extends classical inductive logic. The logic is shown to validate several ... More


The Ontology and Logic of Higher-Order Multitudes

Peter Simons

in Unity and Plurality: Logic, Philosophy, and Linguistics

Published in print:
2016
Published Online:
June 2016
ISBN:
9780198716327
eISBN:
9780191785030
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198716327.003.0004
Subject:
Philosophy, Philosophy of Language

This chapter argues on the basis of examples, and the crucial role of difference as a generating notion, for the ontological acceptance of higher-order multitudes, that is, multitudes whose members ... More


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