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Mathematics | Analysis and Synthesis of Logics - How to Cut and Paste Reasoning Systems

Analysis and Synthesis of Logics

How to Cut and Paste Reasoning Systems

Series: Applied Logic Series, Vol. 35

Carnielli, W., Coniglio, M., Gabbay, D.M., Gouveia, P., Sernadas, C.

2008, XVI, 602 p.

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  • First book addressing both composition and decomposition of logics
  • Tool box for combining and decomposing logics in different guises
  • Mathematical approach
  • Several examples in such diverse areas as software specification, knowledge representation, argumentation theory, networks, security protocols and quantum computing
  • Written by internationally leading researchers in the field of pure and applied logic and philosophy

Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature (for instance, two Hilbert calculi or a Hilbert calculus and a tableau calculus). The important issue of preservation of properties is extensively addressed. For instance, sufficient conditions are provided for a combined logic to be sound and complete when the original component logics are known to be sound and complete.

The book brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). It also provides examples of potential applications in emergent fields like security protocols, quantum computing, networks and argumentation theory, besides discussing more classical applications like software specification, knowledge representation, computational linguistics and modular automated reasoning.

This monograph will be of interest to researchers and graduate students in mathematical logic, theory of computation and philosophical logic with no previous knowledge of the subject of combining and decomposing logics, but with a working knowledge of first-order logic. The book will also be relevant for people involved in research projects where logic is used as a tool and the need for working with several logics at the same time is mandatory (for instance, temporal, epistemic and probabilistic logics).

Content Level » Research

Keywords » Argumentation Theory - Combination of logics - Decomposition of logics - Fibring of logics - Network fibring - Preservation of properties - logic - mathematical logic - predicate logic

Related subjects » Logic & Philosophy of Language - Mathematics - Theoretical Computer Science

Table of contents 

Introductory overview.- Splicing logics: Syntactic fibring.- Splicing logics: Semantic fibring.- Heterogeneous fibring.- Fibring non-truth functional logics.- Fibring first-order logics.- Fibring higher-order logics.- Modulated fibring.- Splitting logics.- New trends: Network fibring.- Summing-up and outlook.

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