The Experts below are selected from a list of 39 Experts worldwide ranked by ideXlab platform
Bartosz Więckowski - One of the best experts on this subject based on the ideXlab platform.
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RULES FOR SUBAtomic DERIVATION
Review of Symbolic Logic, 2011Co-Authors: Bartosz WięckowskiAbstract:In proof-theoretic semantics the meaning of an Atomic Sentence is usually determined by a set of derivations in an Atomic system which contain that Sentence as a conclusion (see, in particular, Prawitz, 1971, 1973). The paper critically discusses this standard approach and suggests an alternative account which proceeds in terms of subAtomic introduction and elimination rules for Atomic Sentences. A simple subAtomic normal form theorem by which this account of the semantics of Atomic Sentences and the terms from which they are composed is underpinned, shows moreover that the proof-theoretic analysis of first-order logic can be pursued also beneath the Atomic level.
Agustin Rayo - One of the best experts on this subject based on the ideXlab platform.
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Absolute Generality Reconsidered
2012Co-Authors: Agustin RayoAbstract:Years ago, when I was young and reckless, I believed that there was such a thing as an allinclusive domain. Now I have come to see the error of my ways. The source of my mistake was a view that might be labeled ‘Tractarianism’. Tractarians believe that language is subject to a metaphysical constraint. In order for an Atomic Sentence to be true, there needs to be a certain kind of correspondence between the semantic structure of the Sentence and the ‘metaphysical structure’ of reality. The purpose of this paper is to explain why I think Tractarianism is mistaken, and what I think an anti-Tractarian should say about absolutely general quantification.
Tor Sandqvist - One of the best experts on this subject based on the ideXlab platform.
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Base-extension semantics for intuitionistic sentential logic
Logic Journal of The Igpl \ Bulletin of The Igpl, 2015Co-Authors: Tor SandqvistAbstract:Intuitionistic sentential logic is shown to be sound and complete with respect to a semantics centered around extensions of Atomic bases (i.e. sets of inference rules for Atomic Sentences). The result is made possible through a non-standard interpretation of disjunction, whereby, roughly speaking, a disjunction is taken to hold just in case every Atomic Sentence that follows from each of the disjuncts separately holds; it is argued that this interpretation makes good sense provided that rules in Atomic bases are conceived of as being accepted hypothetically rather than categorically.
Giacomo Bonanno - One of the best experts on this subject based on the ideXlab platform.
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The logical representation of extensive games
International Journal of Game Theory, 1993Co-Authors: Giacomo BonannoAbstract:Given an extensive formG, we associate with every choice an Atomic Sentence and with every information set a set of well-formed formulas (wffs) of prepositional calculus. The set of such wffs is denoted by Γ(G). Using the so-called topological semantics for propositional calculus (which differs from the standard one based on truth tables), we show that the extensive form yields a topological model of Γ(G), that is, every wff in Γ(G), is “true in G”. We also show that, within the standard truth-table semantics for propositional calculus, there is a one-to-one and onto correspondence between the set of plays ofG and the set of valuations that satisfy all the wffs in Γ(G).
I.b. Turksen - One of the best experts on this subject based on the ideXlab platform.
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Canonical forms of fuzzy truthoods by meta-theory based upon modal logic
Information Sciences, 2020Co-Authors: Gernmano Resconi, I.b. TurksenAbstract:In this paper, we redefine, with the meta-theory based on modal logic, the operations between fuzzy sets of verity, i.e., fuzzy sets of truthood. With this new approach, we can unify the different formulas for the operations AND, OR and NOT between the fuzzy sets of verity, i.e., truthood. The operations between the fuzzy sets of verity become sensitive to the logic value true or false that agents, persons, sensors, assign to the worlds (contexts). The operations are also sensitive to the difference of the worlds and time of synchronisation. It should be pointed out that when we use the logic operations as AND, OR and NOT, we generally assume that the worlds are the same and change their truth-value at the same time. But it is known that there are cases where this synchronic situation and identity is not always valid. That is, there exist transformations that change one world for one proposition to another world for another proposition. In conclusion, the linguistic AND, OR, NOT operations become dependent on the particular truth-value of a world, on the synchronisation and on the worlds assigned to the two propositions via transformations. Thus all of these possible changes in the structure of the worlds, in the modal logic, cause the gradation of the linguistic operations, e.g., AND, OR, and NOT. An individual world (person, agent, sensor, …) assigns to an Atomic Sentence either a true or false value and uses the classical two value logic operations of AND, OR, NOT. That is the crisp true or false responses (assignments) of worlds generate gradation of truthood value. The uncertainty in a fuzzy set is represented with sets of worlds in a conflict situation, i.e., the same proposition may be true in one world and false in another. Consonant or dissonant relations between sets of worlds that depends on the synchronisation and/or transformation of worlds cause the generation of gradation by the linguistic operations AND OR and NOT. That is, the linguistic operations change for different concrete situations (set of worlds) caused by the generation of a representation in each world, where the “descriptive” set membership assignment D may be two or infinite valued but the “verity” assignment V is two-valued in a particular world representation. Whereas membership values of the fuzzy set of truth verifications associated with the set of worlds are in [0,1]. Furthermore, the combination of fuzzy membership values generates a Type II fuzzy set that is captured by FDCF and FCCF formulas. In this paper, we show that there exist a deeper connection between the set membership assignment and the verity assignment of truthood by modal logic with suitable extensions.
