1  10
 Queiroz, Ruy J. G. B. de.
 Hackensack, N.J. : World Scientific, c2012.
 Description
 Book — xxxii, 266 p. : ill ; 24 cm.
 Summary

This comprehensive book provides an adequate framework to establish various calculi of logical inference. Being an 'enriched' system of natural deduction, it helps to formulate logical calculi in an operational manner. By uncovering a certain harmony between a functional calculus on the labels and a logical calculus on the formulas, it allows mathematical foundations for systems of logic presentation designed to handle metalevel features at the objectlevel via a labelling mechanism, such as the D Gabbay's Labelled Deductive Systems. The book truly demonstrates that introducing of 'labels' is useful to understand the proofcalculus itself, and also to clarify its connections with modeltheoretic interpretations.
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA9 .Q45 2012  Unknown 
 Queiroz, Ruy J. G. B. de.
 Singapore : World Scientific, ©2012.
 Description
 Book — 1 online resource (xxxii, 266 pages).
 Summary

 1. Labelled natural deduction. 1.1. The role of the labels. 1.2. Canonical proofs and normalisation
 2. The functional interpretation of implication. 2.1. Introduction. 2.2. Origins. 2.3. Types and propositions. 2.4. [symbol]abstraction and implication. 2.5. Consistency proof. 2.6. Systems of implication and combinators. 2.7. Finale
 3. The existential quantifier. 3.1. Motivation. 3.2. Quantifiers and normalisation. 3.3. Other approaches to existential quantification. 3.4. Modeltheoretic semantics. 3.5. Finale. 3.6. Examples of deduction
 4. Normalisation. 4.1. Introduction. 4.2. Proof transformations in labelled deduction. 4.3. Equivalences between proofs in LND. 4.4. The term rewriting system for LND. 4.5. Examples of transformations between proofs. 4.6. Final remarks
 5. Natural deduction for equality. 5.1. Introduction. 5.2. Labelled deduction. 5.3. Finale
 6. Normalisation for the equality fragment. 6.1. General rules. 6.2. The 'subterm substitution' rule. 6.3. The [symbol] and [symbol]rules. 6.4. Term rewriting systems. 6.5. The transformations between proofs in the equational fragment of the LND. 6.6. The rewriting system for the LND equational logic. 6.7. The normalization procedure: some examples. 6.8. Final remarks. 6.9. Appendix: The [symbol] and [symbol]reductions for the LND system. 6.10. Termination property for LND(EQ)TRS
 7. Modal logics. 7.1. The functional interpretation. 7.2. Modal logics and the functional interpretation. 7.3. Finale
 8. Meaning and proofs: a reflection on prooftheoretic semantics. 8.1. Prooftheoretic semantics. 8.2. Meaning, use and consequences. 8.3. Meaning and purpose. 8.4. Meaning and use. 8.5. Meaning and the explanation of consequences. 8.6. Use and the explanation of consequences. 8.7. Early signs of 'meaninguse/usefulnessconsequences'. 8.8. Normalisation of proofs: the explanation of the consequences. 8.9. Concluding remarks.
3. Explanatory nonmonotonic reasoning [2005]
 Bochman, Alexander, 1955
 Hackensack, NJ : World Scientific, ©2005.
 Description
 Book — 1 online resource (xiv, 408 pages) Digital: data file.
 Summary

 Scott Consequence Relations
 Biconsequence Relations
 FourValued Logics
 Nonmonotonic Semantics
 Default Consequence Relations
 Argumentation Theory
 Production and Causal Inference
 Epistemic Consequence Relations
 Modal Nonmonotonic Logics.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Bochman, Alexander, 1955
 Hackensack, NJ : World Scientific, c2005.
 Description
 Book — 1 online resource (xiv, 408 p.)
 Summary

 Scott Consequence Relations
 Biconsequence Relations
 FourValued Logics
 Nonmonotonic Semantics
 Default Consequence Relations
 Argumentation Theory
 Production and Causal Inference
 Epistemic Consequence Relations
 Modal Nonmonotonic Logics.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
5. Reasoning about theoretical entities [2003]
 Forster, T. E.
 River Edge, N.J. : World Scientific, ©2003.
 Description
 Book — 1 online resource (93 pages)
 Summary

 Definite Descriptions
 Virtual Objects
 Cardinal Arithmetic
 The Canonical Simulation
 Iterated Virtuality in Cardinal Arithmetic
 Ordinals.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Forster, T. E.
 River Edge, N.J. : World Scientific, c2003.
 Description
 Book — 1 online resource (93 p.)
 Summary

 Definite Descriptions
 Virtual Objects
 Cardinal Arithmetic
 The Canonical Simulation
 Iterated Virtuality in Cardinal Arithmetic
 Ordinals.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Frias, Marcelo Fabián, 1968
 River Edge, NJ : World Scientific, 2002.
 Description
 Book — 1 online resource (xi, 217 pages) Digital: data file.
 Summary

 Ch. 1. Introduction and motivations. 1.1. Software specification, binary relations and fork
 ch. 2. Algebras of binary relations and relation algebras. 2.1. History and definitions. 2.2. Arithmetical properties
 ch. 3. Proper and abstract fork algebras. 3.1. On the origin of fork algebras. 3.2. Definition of the classes. 3.3. Arithmetical properties
 ch. 4. Representability and independence. 4.1. Representability of abstract fork algebras. 4.2. Independence of the axiomatization of fork
 ch. 5. Interpretability of classical firstorder logic. 5.1. Basic definitions. 5.2. Interpreting FOLE
 ch. 6. Algebraization of nonclassical logics. 6.1. Basic definitions and properties. 6.2. The fork logic FL. 6.3. Modal logics. 6.4. Representation of constraints in FL. 6.5. Interpretability of modal logics in FL. 6.6. A proof theoretical approach. 6.7. Interpretability of propositional dynamic logic in FL. 6.8. The fork logic FL'. 6.9. A RasiowaSikorski calculus for FL'. 6.10. A relational proof system for intuitionistic logic. 6.11. A relational proof system for minimal intuitionistic logic. 6.12. Relational reasoning in intermediate logics
 ch. 7. A calculus for program construction. 7.1. Introduction. 7.2. Filters and sets. 7.3. The relational implication. 7.4. Representability and expressiveness in program construction. 7.5. A methodology for program construction. 7.6. Examples. 7.7. A D & C algorithm for MAXSTA. 7.8. Comparison with previous work.
 Frias, Marcelo Fabián, 1968
 River Edge, NJ : World Scientific, c2002.
 Description
 Book — xi, 217 p. ; 24 cm.
 Summary

 Contents: Introduction and Motivations
 Algebras of Binary Relations and Relation Algebras
 Proper and Abstract Fork Algebras
 Representability and Independence
 Interpretability of Classical FirstOrder Logic
 Algebraization of NonClassical Logics
 A Calculus for Program Construction.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
SAL3 (offcampus storage)
SAL3 (offcampus storage)  Status 

Stacks  Request (opens in new tab) 
QA76.9 .M35 F75 2002  Available 
9. Essays on nonclassical logic [2001]
 River Edge, N.J. : World Scientific, ©2001.
 Description
 Book — 1 online resource (xi, 262 pages) : illustrations
 Summary

 FineGrained Theories of Time (P Blackburn)
 Revision Sequences and Computers with an Infinite Amount of Time (B Lowe)
 On Frege's Nightmare: A Combination of Intuitionistic, Free and Paraconsistent Logics (S Rahman)
 Truthmakers, Entailment and Necessity (S Read)
 Global Definability in Basic Modal Logic (M de Rijke & H Sturm)
 Ackermann's Implication for Typefree Logic (K Robering)
 Why Dialogical Logic? (H Ruckert)
 Semantics for Constructive Negations (Y Shramko)
 Recent Trends in Paraconsistent Logic (M Urchs)
 Obligations, Authorities, and History Dependence (H Wansing).
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Singapore ; River Edge, N.J. : World Scientific Pub. Co., c2001.
 Description
 Book — xi, 262 p. : ill.
 Summary

 FineGrained Theories of Time (P Blackburn)
 Revision Sequences and Computers with an Infinite Amount of Time (B Lowe)
 On Frege's Nightmare: A Combination of Intuitionistic, Free and Paraconsistent Logics (S Rahman)
 Truthmakers, Entailment and Necessity (S Read)
 Global Definability in Basic Modal Logic (M de Rijke & H Sturm)
 Ackermann's Implication for Typefree Logic (K Robering)
 Why Dialogical Logic? (H Ruckert)
 Semantics for Constructive Negations (Y Shramko)
 Recent Trends in Paraconsistent Logic (M Urchs)
 Obligations, Authorities, and History Dependence (H Wansing).
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
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