Complexity of Two-Variable Dependence Logic and IF-Logic

Complexity of two-variable dependence logic and IF-logic

Information and Computation ◽

10.1016/j.ic.2014.08.004 ◽

2014 ◽

Vol 239 ◽

pp. 237-253 ◽

Cited By ~ 5

Author(s):

Juha Kontinen ◽

Antti Kuusisto ◽

Peter Lohmann ◽

Jonni Virtema

Keyword(s):

Dependence Logic ◽

If Logic

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Kant and the Science of Logic

10.1093/oso/9780190907136.001.0001 ◽

2018 ◽

Cited By ~ 3

Author(s):

Huaping Lu-Adler

Keyword(s):

History Of Philosophy ◽

Logical Pluralism ◽

Philosophy Of Logic ◽

Science Of Logic ◽

Transcendental Logic ◽

If Logic ◽

General Logic ◽

Two Factors ◽

History Of ◽

Philosophical Debates

This book is both a history of philosophy of logic told from the Kantian viewpoint and a reconstruction of Kant’s theory of logic from a historical perspective. Kant’s theory represents a turning point in a history of philosophical debates over the following questions: (1) Is logic a science, instrument, standard of assessment, or mixture of these? (2) If logic is a science, what is the subject matter that differentiates it from other sciences, particularly metaphysics? (3) If logic is a necessary instrument to all philosophical inquiries, how is it so entitled? (4) If logic is both a science and an instrument, how are these two roles related? Kant’s answer to these questions centers on three distinctions: general versus particular logic, pure versus applied logic, pure general logic versus transcendental logic. The true meaning and significance of each distinction becomes clear, this book argues, only if we consider two factors. First, Kant was mindful of various historical views on how logic relates to other branches of philosophy (viz. metaphysics and physics) and to the workings of common human understanding. Second, he first coined “transcendental logic” while struggling to secure metaphysics as a proper “science,” and this conceptual innovation would in turn have profound implications for his mature theory of logic. Against this backdrop, the book reassesses the place of Kant’s theory in the history of philosophy of logic and highlights certain issues that are still debated today, such as normativity of logic and the challenges posed by logical pluralism.

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QUANTUM TEAM LOGIC AND BELL’S INEQUALITIES

The Review of Symbolic Logic ◽

10.1017/s1755020315000192 ◽

2015 ◽

Vol 8 (4) ◽

pp. 722-742 ◽

Cited By ~ 17

Author(s):

TAPANI HYTTINEN ◽

GIANLUCA PAOLINI ◽

JOUKO VÄÄNÄNEN

Keyword(s):

Quantum Mechanics ◽

Completeness Theorem ◽

Probability Logic ◽

Bell’S Inequalities ◽

Dependence Logic ◽

Logical Approach ◽

Team Semantics ◽

Bell's Inequalities

AbstractA logical approach to Bell’s Inequalities of quantum mechanics has been introduced by Abramsky and Hardy (Abramsky & Hardy, 2012). We point out that the logical Bell’s Inequalities of Abramsky & Hardy (2012) are provable in the probability logic of Fagin, Halpern and Megiddo (Fagin et al., 1990). Since it is now considered empirically established that quantum mechanics violates Bell’s Inequalities, we introduce a modified probability logic, that we call quantum team logic, in which Bell’s Inequalities are not provable, and prove a Completeness theorem for this logic. For this end we generalise the team semantics of dependence logic (Väänänen, 2007) first to probabilistic team semantics, and then to what we call quantum team semantics.

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The joys of independence: Some uses of IF logic

The Principles of Mathematics Revisited ◽

10.1017/cbo9780511624919.005 ◽

1996 ◽

pp. 72-87

Keyword(s):

If Logic

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Cylindric Set Algebras and IF Logic

Bolyai Society Mathematical Studies - Cylindric-like Algebras and Algebraic Logic ◽

10.1007/978-3-642-35025-2_17 ◽

2013 ◽

pp. 351-366

Author(s):

Allen L. Mann

Keyword(s):

If Logic ◽

Cylindric Set Algebras

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What Would a Phenomenology of Logic Look Like?

Mind ◽

10.1093/mind/fzaa031 ◽

2019 ◽

Vol 129 (516) ◽

pp. 1009-1031

Author(s):

James Kinkaid

Keyword(s):

Logical Consequence ◽

Philosophy Of Logic ◽

Contemporary Philosophy ◽

Consequence Relations ◽

Consequence Relation ◽

If Logic ◽

Pure Logic ◽

Logical Investigations ◽

Normative Status ◽

Selection Of

Abstract The phenomenological movement begins in the Prolegomena to Husserl’s Logical Investigations as a philosophy of logic. Despite this, remarkably little attention has been paid to Husserl’s arguments in the Prolegomena in the contemporary philosophy of logic. In particular, the literature spawned by Gilbert Harman’s work on the normative status of logic is almost silent on Husserl’s contribution to this topic. I begin by raising a worry for Husserl’s conception of ‘pure logic’ similar to Harman’s challenge to explain the connection between logic and reasoning. If logic is the study of the forms of all possible theories, it will include the study of many logical consequence relations; by what criteria, then, should we select one (or a distinguished few) consequence relation(s) as correct? I consider how Husserl might respond to this worry by looking to his late account of the ‘genealogy of logic’ in connection with Gurwitsch’s claim that ‘[i]t is to prepredicative perceptual experience … that one must return for a radical clarification and for the definitive justification of logic’. Drawing also on Sartre and Heidegger, I consider how prepredicative experience might constrain or guide our selection of a logical consequence relation and our understanding of connectives like implication and negation.

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Multiverse—Too Much or Not Enough?

Universe ◽

10.3390/universe5050113 ◽

2019 ◽

Vol 5 (5) ◽

pp. 113 ◽

Cited By ~ 4

Author(s):

Michael Heller

Keyword(s):

Philosophy Of Science ◽

Infinite Number ◽

Category Theory ◽

Explanatory Power ◽

Point Of View ◽

Anthropic Principle ◽

Philosophical Perspective ◽

Einstein's Equations ◽

If Logic ◽

The Way

The aim of this essay is to look at the idea of the multiverse—not so much from the standpoint of physics or cosmology, but rather from a philosophical perspective. The modern story of the multiverse began with Leibniz. Although he treated “other worlds” as mere possibilities, they played an important role in his logic. In a somewhat similar manner, the practice of cosmology presupposes a consideration of an infinite number of universes, each being represented by a solution to Einstein’s equations. This approach prepared the way to the consideration of “other universes” which actually exist, first as an auxiliary concept in discussing the so-called anthropic principle, and then as real universes, the existence of which were supposed to solve some cosmological conundrums. From the point of view of the philosophy of science, the question is: Could the explanatory power of a multiverse ideology compensate for the relaxation of empirical control over so many directly unobservable entities? It is no surprise that appealing to a possibly infinite number of “other universes” in order to explain some regularities in our world would seem “too much” for a self-disciplined philosopher. With no strict empirical control at our disposal, it is logic that must be our guide. Also, what if logic changes from one world to another in the multiverse? Such a possibility is suggested by the category theory. From this point of view, our present concepts of the multiverse are certainly “not enough”. Should this be read as a warning that the learned imagination can lead us too far into the realms of mere possibilities?

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