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Natural Deduction

(2015)

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  1. A Modal View on Resource-Bounded Propositional Logics.Pere Pardo - 2022 - Studia Logica 110 (4):1035-1080.
    Classical propositional logic plays a prominent role in industrial applications, and yet the complexity of this logic is presumed to be non-feasible. Tractable systems such as depth-bounded boolean logics approximate classical logic and can be seen as a model for resource-bounded agents whose reasoning style is nonetheless classical. In this paper we first study a hierarchy of tractable logics that is not defined by depth. Then we extend it into a modal logic where modalities make explicit the assumptions discharged in (...)
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  • Proof Theory for Modal Logic.Sara Negri - 2011 - Philosophy Compass 6 (8):523-538.
    The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective.
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  • A Model for Creation: Part I.Paul Bernard White - manuscript
    Four initial postulates are presented (with two more added later), which state that construction of the physical universe proceeds from a sequence of discrete steps or "projections" --- a process that yields a sequence of discrete levels (labeled 0, 1, 2, 3, 4). At or above level 2 the model yields a (3+1)-dimensional structure, which is interpreted as ordinary space and time. As a result, time does not exist below level 2 of the system, and thus the quantum of action, (...)
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  • A Model for Constructing the Physical Universe.White Paul - manuscript
    In the introduction I argue that the basic element (or primitive) for constructing the physical universe is "displacement from a prior level", and the basic structure is "a sequence of such displacements" (summarized as postulates 1 and 2). The displacements are then defined as one-dimensional objects with a direction (postulate 3). The relations between these displacements are stated in postulate 4. In section 2 we discuss basic consequences of the postulates, and in section 3 we use the postulates to derive (...)
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  • A Model for Creation: Part II.Paul Bernard White - manuscript
    In Part I we developed a model, called system P, for constructing the physical universe. In the present paper (Part II) we explore the hypothesis that something exists prior to the physical universe; i.e. we suppose that there exists a sequence of projections (and levels) that is prior to the sequence that constructs the physical universe itself. To avoid an infinite regress, this prior sequence must be finite, meaning that the whole chain of creative projections must begin at some primal (...)
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