191 research outputs found
Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics
We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer
and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We
give new analytic proof systems for A and use the embeddings to derive
corresponding systems for L. These include: hypersequent calculi for A and L
and terminating versions of these calculi; labelled single sequent calculi for
A and L of complexity co-NP; unlabelled single sequent calculi for A and L.Comment: 35 pages, 1 figur
Sequent and hypersequent calculi for abelian and łukasiewicz logics
We present two embeddings of Łukasiewicz logicŁinto Meyer and Slaney's Abelian logicA, the logic of lattice-ordered Abelian groups. We give new analytic proof systems forAand use the embeddings to derive corresponding systems forŁ. These include hypersequent calculi, terminating hypersequent calculi, co-NP labeled sequent calculi, and unlabeled sequent calculi
Multivalued Logic, Neutrosophy and Schrodinger equation
This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given. Neutrosophy itself was developed in attempt to generalize Fuzzy-Logic introduced by L. Zadeh. While some aspects of theoretical foundations of logic are discussed, this book is not intended solely for pure mathematicians, but instead for physicists in the hope that some of ideas presented herein will be found useful. The book is motivated by observation that despite almost eight decades, there is indication that some of those paradoxes known in Quantum Physics are not yet solved. In our knowledge, this is because the solution of those paradoxes requires re-examination of the foundations of logic itself, in particular on the notion of identity and multi-valuedness of entity.
The book is also intended for young physicist fellows who think that somewhere there should be a ‘complete’ explanation of these paradoxes in Quantum Mechanics. If this book doesn’t answer all of their questions, it is our hope that at least it offers a new alternative viewpoint for these old questions
Decision Problems for Partial Specifications: Empirical and Worst-Case Complexities
Partial specifications allow approximate models of systems such as Kripke structures, or labeled
transition systems to be created. Using the abstraction possible with these models, an avoidance
of the state-space explosion problem is possible, whilst still retaining a structure that can
have properties checked over it. A single partial specification abstracts a set of systems, whether
Kripke, labeled transition systems, or systems with both atomic propositions and named transitions.
This thesis deals in part with problems arising from a desire to efficiently evaluate
sentences of the modal μ-calculus over a partial specification.
Partial specifications also allow a single system to be modeled by a number of partial specifications,
which abstract away different parts of the system. Alternatively, a number of partial
specifications may represent different requirements on a system. The thesis also addresses the
question of whether a set of partial specifications is consistent, that is to say, whether a single
system exists that is abstracted by each member of the set. The effect of nominals, special
atomic propositions true on only one state in a system, is also considered on the problem of the
consistency of many partial specifications. The thesis also addresses the question of whether
the systems a partial specification abstracts are all abstracted by a second partial specification,
the problem of inclusion.
The thesis demonstrates how commonly used “specification patterns” – useful properties specified
in the modal μ-calculus, can be efficiently evaluated over partial specifications, and gives
upper and lower complexity bounds on the problems related to sets of partial specifications
Fuzzy expert systems in civil engineering
Imperial Users onl
Foundations of Fuzzy Logic and Semantic Web Languages
This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic
Foundations of Fuzzy Logic and Semantic Web Languages
This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic
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