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Nonclassical mathematical logic --- Rationalism

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Nonclassical mathematical logic --- Congresses --- Electronic data processing --- Electronic digital computers

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This book presents a comprehensive, non-model-theoretic theory of ontic necessity and possibility within a formal (and formalized) ontology consisting of states of affairs, properties, and individuals. Its central thesis is that all modalities are reducible to intrinsic (or "logical") possibility and necessity if reference is made to certain states of affairs, called "bases of necessity." The viability of this Bases-Theory of Modality is shown also in the case of conditionals, including counterfactual conditionals. Besides the ontological aspects of the philosophy of modality, also the epistemology of modality is treated in the book. It is shown that the Bases-Theory of Modality provides a satisfactory solution to the epistemological problem of modality. In addition to developing that theory, the book includes detailed discussions of positions in the philosophy of modality maintained by Alvin Plantinga, David Lewis, Charles Chihara, Graeme Forbes, David Armstrong, and others. Among the themes treated are: possibilism vs. actualism; the theory of essences; conceivability and possibility; the nature of possible worlds; the nature of logical, nomological, and metaphysical possibility and necessity.

Modality (Logic) --- Modal logic --- Logic --- Nonclassical mathematical logic --- Bisimulation

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This book on modal logic is especially designed for philosophy students. It provides an accessible yet technically sound treatment of modal logic and its philosophical applications. Every effort is made to simplify the presentation by using diagrams instead of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dicto distinction. Discussion of philosophical issues concerning the development of modal logic is woven into the text. The book uses natural deduction systems, which are widely regarded as the easiest to teach and use. It also includes a diagram technique that extends the method of truth trees to modal logic. This provides a foundation for a novel method for showing completeness that is easy to extend to quantifiers. This second edition contains a new chapter on logics of conditionals, an updated and expanded bibliography, and is updated throughout. A number of technical results have also been clarified and streamlined.

Modality (Logic) --- Modal logic --- Logic --- Nonclassical mathematical logic --- Bisimulation

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Modality (Logic) --- Modal logic --- Logic --- Nonclassical mathematical logic --- Bisimulation