A Manual of Intensional Logic
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I. Classical Theories
1 Tense and Time
2 Modality
3 Conditionals
4 Combinations
II. Recent Developments 1: Computational Applications
5 Mathematics and Computer Sience
III. Recent Developments 2: Partialilty
6 Intervals and Events
7 Possibility and Information
8 The Logic of Partiality
IV. Recent Developments 3: Logical Semantics
9 Denotational Constraints on Tense and Modality
10 Conditionals as Generalized Quantifiers
11 Intensions ...
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Lectures on Linear Logic
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2 Sequent calculus for linear logic
3 Some elementary syntactic results
4 The calculus of two implications
5 Embeddings and approximations
6 Natural deduction systems for linear logic
7 Hillbert-type systemens
8 Algebraic semantics
9 Combinational linear logic
10 Girard domains
11 Coherence in symmetric monoidal
12 The storage operator as a cofree comonoid
13 Evaluation in typed calculii
14 Computation by lazy evaluation in CCC's
15 Computatio...
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Metamathematics of First-Order Arithmetic
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PART A
I - Arithmetic as Number Theory, Set Theory and Logic
II - Fragments and Combinatorics
PART B
III - Self-Reference
IV - Models of Fragments of Arithmetic
PART C
V - Bounded Arithmetic
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Modal Logic - An Introduction
Modal Logic - An IntroductionBrian F. ChellasPART I
1 - Introduction
2 - Logical preliminaries
PART II
3 - Standard models for modal logics
4 - Normal systems of modal logic
5 - Determination and decidability for normal systems
6 - Deontic Logic
PART III
7 - Minimal models for modal logics
8 - Classical systems of modal logic
9 - Determination and decidability for classical systems
10 - Conditional logic
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Mathematics of Modality
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1: Metamathematics of Modal Logic
2: Semantic Analysis of Orthologic
3: Orthomodularity is not Elementary
4: Arithmetical Necessity, Provability and Intuitionistic Logic
5: Diodorean Modality in Minkowski Spacetime
6: Grothendieck Topology as Geometric Modality
7: The Semantics of Hoare’s Iteration Rule
8: An Abstract Setting for Henkin Proofs
9: A Framework for Infinitary Modal Logic
10: The McKinsey Axiom Is Not Canonical
11: Elementary Log...
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An Introduction to Modal Logic
An Introduction to Modal LogicG.E. Hughes, M.J. CresswellI. Modal Propositional Logic
II. Modal Predicate Logic
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The Axiom of Choice
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1. Introduction
2. Use of the axiom of choice
3. Consistency of the axiom of choice
4. Permutation models
5. Independence of the axiom of choice
6. Embedding theorems
7. Models with finite supports
8. Some weaker versions of the axiom of choice
9. Nontransferable statements
10. Mathematics without choice
11. Cardinal numbers in set theory without choice
12. Some properties contradicting the axiom of choice
Appendix 1. Equivalents of the axiom of choice
Ap...
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Elements of Intuitionism
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2. Elementary Intuitionistic Mathematics
3. Choice Sequences and Spreads
4. The Formalization of Intuitionistic Logic
5. The Semantics of Intuitionistic Logic
6. Some Further Topics
7. Concluding Philosophical Remarks
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Intuitionism - An Introduction
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II. Arithmetic
III. Spreads and species
IV. Algebra
V. Plane pointspecies
VI. Measure and integration
VII. Logic
VIII. Controversial subjects
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The Principles of Mathematics Revised
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2 - The game of logic
3 - Frege's fallacy foiled: Independence-friendly logic
4 - The joys of independence: Some uses of IF logic
5 - The complexities of completeness
6 - Who's afraid of Alfred Tarski? Truth definitions for IF first-order languages
7 - The liar belied: Negation in IF logic
8 - Axiomatic set theory: Fraenkelstein's monster?
9 - IF logic as a framework for mathematica...
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On Formally Undecidable Propositions Of Principia Mathematica And Related Systems
On Formally Undecidable Propositions Of Principia Mathematica And Related SystemsKurt GödelIn 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Gödel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will ...
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Proof Theory
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1. First Order Predicate Calculus
2. Peano Arithmetic
Part II. Second Order and Finite Order Systems
3. Second Order Systems and Simple Type Theory
4. Infinitary Logic
Part III. Consistency Problems
5. Consistency Proofs
6. Some Applications of Consistency Proofs
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Structural Proof Theory
Structural Proof TheorySara Negri, Jan von PlatoPREFACE
INTRODUCTION
1 FROM NATURAL DEDUCTION TO SEQUENT CALCULUS
2 SEQUENT CALCULUS FOR INTUITIONISTIC LOGIC
3 SEQUENT CALCULUS FOR INTUITIONISTIC LOGIC
4 THE QUANTIFIERS
5 VARIANTS OF SEQUENT CALCULI
6 STRUCTURAL PROOF ANALYSIS OF AXIOMATIC THEORIES
7 INTERMEDIATE LOGICAL SYSTEMS
8 BACK TO NATURAL DEDUCTION
CONCLUSION: DIVERSITY AND UNITY IN STRUCTURAL PROOF THEORY
APPENDIX A SIMPLE TYPE THEORY AND CATEGORIAL GRAMMAR
APPENDIX B PROOF THEORY AND C...
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Normalization, Cut-Elimination and the Theory of Proofs
Normalization, Cut-Elimination and the Theory of ProofsA.M. UngarIntroduction
1 Background
2 Comparing NJ with LJ
3 Natural Deduction Revisited
4 The Problem of Substitution
5 A Multiple-Conclusion Calculus
6 Reduction Procedures
7 Correspondence Results
8 Interpretations of Derivations
Appendices
A. A Strong Cut-Elimination Theorem for LJ
B. A Formulation of the Classical Sequent Calculus
C. Proofs and Categories
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Model Theory
Model TheoryC.C. Chang, H. Jerome Keisler1. Introduction
2. Models constructed from constants
3. Further model-theoretic constructions
4. Ultraproducts
5. Saturated and special models
6. More about ultraproducts and generalizations
7. Selected topics
A. Set theory
B. Open problems in classical model theory
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Set Theory - An Introduction to Large Cardinals
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2 The Development of ZFC
3 The Léavy Hierarchy and the Reflection Principle
4 Inaccessible and Mahlo Cardinals
5 The Constructtble Universe
6 Measurable Cardinals
7 Trees and Partition Properties
8 Partition Cardinals and Model Theory: Silver's Results
9 Indescribable Cardinals
10 Infinitary Languages and Large Cardinals
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Set Theory and the Continuum Hypothesis
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IV. The Independence of the Continuum Hypothesis and the Axiom of Choice
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Set Theory
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1. Axiomatic Set Theory
2. Transitive Models of Set Theory
Part II. More Sets
3. Forcing and Generic Models
4. Some Applications of Forcing
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6. Other Large Cardinals
Part IV. Sets of Reals
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Introduction to Combinatorics and λ-Calculus
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2 Combinatory logic
3 The power of λ and combinators
4 Representing the computable functions
5 The undecidability theorem
6 The formal theories λβ and CLw
7 Extensionality in λ-calculus
8 Extensionality in combinatory logic
9 Correspondence between λ and CL
10 Simple typing, Church-style
11 Simple typing, Curry-style in CL
12 Simple typing, Curry-style in λ
13 Generalizations of typing
14 Mo...
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Tense Logic
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3. Branching Tense Logic and Temporal Modality
4. Quantificational Tense Logics
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Introduction to higher order categorical logic
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Logica, etiketten en vlees
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Literaire, logische en vaak satirische bespiegelingen over onderwerpen uit de moderne angelsaksische filosofie.
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De grondslagen der arithmetica
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Beknopte biografie
Noten
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- Inleiding
- Tekst
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Filosofische grondslagen van de wiskunde
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6. Zijn er constanten van het wiskundig denken?
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Logica voor alfa's en informatici
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Logica en model
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Frege and Gödel - Two Fundamental Texts in Mathematical Logic
Frege and Gödel - Two Fundamental Texts in Mathematical LogicJean van Heijenoort (ed.)Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought (1879), by G. Frege
Some metamathematical results on completeness and consistency; On formally undecidable propositions of Principia mathematica and related systems I; and On completeness and consistency (1930b, 1931, and 1931a), by K. Gödel
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Perspectives on the History of Mathematical Logic
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Peirce and the Law of Distribution - Nathan Houser
The First Russell Paradox - Irving H. Anellis
Principia Mathematica and the Development of Automated Theorem Proving - Daniel J. O’Leary
Oswald Veblen and the Origins of Mathematical Logic at Princeton - William Aspray
The Löwenheim-Skolem Theorem, Theories of Quantification, and Proof Theory - Irving H. Anellis...
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A Mathematical Introduction to Logic
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2. First-Order Logic
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4. Second-Order Logic
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Popular Lectures on Mathematical Logic
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Topics include the pl...
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Handbook of Mathematical Logic
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Part B. Set Theory (Contributors: J.P. Burgess, K.J. Devlin, T.J. Jech, I. Juhász, K. Kunen, M.E. Rudin, J.R. Schoenfield)
Part C. Recursion Theory (Contributors: P. Aczel, M. Davis, H.B. Enderton, A. Kechris, D.A. Martin, Y.N. Moschovakis, M.O. Rabin, R.A. Shore, S.G. Simpson)
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Proofs and Refutations - The Logic of Mathematical Discovery
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L.E.J. Brouwer -Een biografie
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3. Mystiek
4. De dissertatie
5. Naar de wiskundige top
6. De universitaire carrière
7. Ontwikkeling in isolement
8. Wetenschap en politiek
9. Het onderzoekscentrum Blaricum
10. Dimensietheorie en grondslagenstrijd
11. Götterdämmerung
12. Verloren jaren
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Leibniz
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De binnenkant der werkelijkheid: de monaden
De buitenkant der werkelijkheid: organisatie, evolutie, perceptie, harmonie
De logica der beste wereld: waarheid, vrijheid, God
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Mersenne and the Learning of the Schools
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4. Aristotelian Science and the Metaphysics of Mathematics
5. Saint Augustine and Universal Harmony
6. Mechanics, Music, and Harmony
7. Philosophical Systems, Essentialism, and the Language of Philosophy
8. Mersenne’s Later Career: A Philosophical Agenda and Its Limitations
9. Summary and Conclusions
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Introduction to Mathematical Logic
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Robot op zee
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De stelling van Gödel
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The Elements of Mathematical Logic
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Een nacht vol opwinding - Een keuze uit de filosofische essays
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3. Uitvinding in de wiskunde
4. Wiskundige definities en onderwijs
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7. Wiskundig concept en ervaring
8. Intuïtie en logica bij wiskunde
9. De evolutie van de wetten
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Formele logica - Een informele inleiding
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Summulae logicales
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Logica voor informatica
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Exacte logica
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Inleiding tot de symbolische logica
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Combinatory Logic, Vol. 1
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6. Synthetic Theory of Combinatorics
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Inleiding tot de Logica
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Quantoren, Modalitäten, Paradoxien - Beiträge zur Logik
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Intuitionism
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III. Spreads and species
IV. Algebra
V. Plane pointspecies
VI. Measure and integration
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VIII. Controversial subjects
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8. De reeks van Taylor
9. Primitieve functies
10. Integraalrekening
11. Determinanten, lineaire vergelijkingen, eliminanten
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13. Puntenparen en kegelsneden
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History of Mathematical Logic from Leibniz to Peano
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Moderne logica
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V. Over de zogenaamde denkmachine
VI. De paradoxen
VII. Verstand en intuïtie
VIII. Geformaliseerde talen en normaal taalgebruik
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Leibniz: Metaphysics and Philosophy of Science
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