The Experts below are selected from a list of 12 Experts worldwide ranked by ideXlab platform
Richmond H. Thomason - One of the best experts on this subject based on the ideXlab platform.
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ISMIS - A Semantic Analysis of Monotonic Inheritance with Roles and Relations
Lecture Notes in Computer Science, 1991Co-Authors: Richmond H. ThomasonAbstract:The paper addresses the problem of specifying Valid reasoning with roles and relations in inheritance networks. A system of (context free) rules is presented for monotonic inheritance networks with isa, identity, role and relational links. The system is then interpreted in a fragment of first-order logic, and the interpretation is shown to be sound and complete. Thus, any conclusion provable from a network is a logically Valid Consequence of the information in the network, and any logically Valid Consequence in the network query language is provable.
H. C. M. De Swart - One of the best experts on this subject based on the ideXlab platform.
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Intuitionism and Intuitionistic Logic
Springer Undergraduate Texts in Philosophy, 2018Co-Authors: H. C. M. De SwartAbstract:Brouwer’s intuitionism is based on quite different philosophical ideas about the nature of mathematical objects than classical mathematics. This intuitionistic point of view results in a different use of language and in a corresponding different intuitionistic logic which is far more subtle than the classical use of language and corresponding classical logic. Nevertheless an intuitionistic deduction system and a notion of intuitionistic deducibility was developed by A. Heyting and it is amazing to see that a small change in the logical axioms, replacing the logical axiom ГГA → A by ГA → (A → B), may have such far reaching Consequences. Since finding (intuitionistic) formal deductions may be difficult, an intuitionistic tableaux based formal deduction system is presented in which the construction of intuitionistic deductions is rather straightforward. The semantics of intuitionistic logic and the notion of (intuitionistic) Valid Consequence are given in terms of (intuitionistic) Kripke models and it is shown that the three notions of intuitionistic Valid Consequence, intuitionistic deducibility and intuitionistic tableau-deducibility are equivalent. Intuitionistic sets are either finite constructions or otherwise, they are (subsets of) construction projects. Spreads are a particular kind of construction project, inducing specific principles which typically do not hold for other sets.
John Woods - One of the best experts on this subject based on the ideXlab platform.
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Ancestor Worship in The Logic of Games. How foundational were Aristotle's contributions?
Baltic International Yearbook of Cognition Logic and Communication, 2013Co-Authors: John WoodsAbstract:Notwithstanding their technical virtuosity and growing presence in mainstream thinking, game theoretic logics have attracted a sceptical question: “Granted that logic can be done game theoretically, but what would justify the idea that this is the preferred way to do it?” A recent suggestion is that at least part of the desired support might be found in the Greek dialectical writings. If so, perhaps we could say that those works possess a kind of foundational significance. The relation of being foundational for is interesting in its own right. In this paper, I explore its ancient applicability to relevant, paraconsistent and nonmonotonic logics, before returning to the question of its ancestral tie, or want of one, to the modern logics of games. 1. LOGIC AND GAME THEORY Since its inception in the early 1940s (von Neumann & Morgenstern 1944), the mathematical theory of games has become something of a boom industry, with a sophisticated and ever expanding literature in many areas of the physical and biological sciences, the behavioural Ancestor Worship in The Logic of Games 2 and social sciences, the formal and computational sciences, and various branches of philosophy. In its appropriation by logic, the game theoretic orientation has two essential features. The first is that the logical particles quantifiers for example are specified by the rules governing how a player in a win-lose game responds to sentences in which the particle in question has a dominant occurrence, depending on which role in the game he occupies. The rules for this are widely referred to as the logical rules different rules for different roles. Consider, for example, the universal quantifier ∀. Its game theoretic provisions are given as follows: Let A[x] be a formula, with x’s occurrence possibly free. Then when one party advances ∀x A[x], the opposing party selects a constant a for x and challenges the first party to defend A[x/a]. The second feature of the game theoretic approach is that the logic’s metalogical properties truth in a model, Valid Consequence, etc. are game theoretically definable via the concept of a winning strategy. For example, given the axiom of choice it is provable that a first order sentence A is true in a model M in the standard truth conditional sense of Tarski just in case there is a winning strategy for the defender of A in a game G(M) (Hodges 1983). The rules that generate winning strategies also include the game’s organizational and attack-and-defend rules; the rules of procedure. Here, too, there are different rules for different roles. These are commonly known as the structural rules. We now have a simple way of characterizing a game theoretic logic. It is a logic governed by these kinds of logical and structural rules. 2. A QUESTION AND A CHALLENGE My project is motivated by a sceptical question posed byWilfrid Hodges and a hopeful challenge issued by Mathieu Marion (Hodges (2004); Marion (2009). The challenge is intended to play a role in arriving at a response to the question. So I begin with the question. Hodges’ Question: In his Stanford Encylopedia entry on logic and games, Hodges writes: In most applications of logical games, the central notion is that of a winning strategy for [the proponent]. Often these strategies (or their existence) turn out to be equivVol. 8: Games, Game Theory
Nelson Blackie - One of the best experts on this subject based on the ideXlab platform.
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Can Einstein’s Special Theory of Relativity be Considered an Accurate Description of Reality?
International Journal of Theoretical and Mathematical Physics, 2019Co-Authors: Nelson BlackieAbstract:This study shows that Einstein’s Special Theory of Relativity is not a complete theory of reality. The theory used non-uniform experiments; thus, its final conclusions are inconsistent with each other. The most obvious of these is the prediction of a positive correlation between mass and speed (mass increment). This allows the possibility for both the kinetic and potential energies of a system in motion to increase simultaneously (since the system gains mass and hence potential energy). On this grand, the study proposed a new theory (or provides corrections in Einstein’s theory). Then, these corrections were used to show that (1): Entangle particles exist in nature as a result of relative motion; (2): matter and wave are dual entity of each other, and (3): because of the law of conservation, space dilation is a Valid Consequence of relative motion just as time dilation is a Valid Consequence of relativity.
