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Philosophy - Logic & Philosophy of Language | Natural Deduction, Hybrid Systems and Modal Logics

Natural Deduction, Hybrid Systems and Modal Logics

Series: Trends in Logic, Vol. 30

Indrzejczak, Andrzej

2010, XXIII, 514p.

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  • The first to show that the scope of application of Natural Deduction systems is far beyond the one usually considered
  • The first comprehensive presentation of hybrid deductive systems mixing Natural Deduction with Resolution
  • The first to label Natural Deduction systems for a wide spectrum of Temporal Logics
  • Provides a detailed presentation of problems connected with the formalization of Logics of linear time
  • Gives a detailed exposition of deductive systems for Hybrid Logics

This volume provides an extensive treatment of Natural Deduction and related types of proof systems, with a focus on the practical aspects of proof methods. The book has two main aims: Its first aim is to provide a systematic and historical survey of the variety of Natural Deduction systems in Classical and Modal Logics. The second aim is to present some systems of hybrid character, mixing Natural Deduction with other kinds of proof methods (including Sequent systems, Tableaux, Resolution). Such systems tend to be more universal and effective, because of the possibility of mixing strategies of proof search from different areas. All necessary background material is provided, in particular, a detailed presentation of Modal Logics, including First-Order Modal and Hybrid Modal Logics. The deduction systems presented in the book may be of interest to working logicians, researchers on automated deduction and teachers of logic.

Content Level » Research

Keywords » Classical logic - Frames - Hybrid logics - Hybrid systems - Natural deduction - Proof theory - Racter - Resolution - Temporal logics - logic - modal logic - proving

Related subjects » Artificial Intelligence - Computational Science & Engineering - Logic & Philosophy of Language - Mathematics - Theoretical Computer Science

Table of contents 

Preliminaries.- Standard Natural Deduction.- Other Deductive Systems.- Extended Natural Deduction.- Survey of Modal Logics.- Standard Approach to Basic Modal Logics.- Beyond Basic Logics and Standard Systems.- Labelled Systems in Modal Logics.- Logics of Linear Frames.- Analytic Labelled ND and Proof Search.- Modal Hybrid Logics.- Proof Methods for MHL.

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