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A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS (fourth edition)
, 2005
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A Behavioural Model For Linguistic Uncertainty
 INFORMATION SCIENCES
, 1998
"... The paper discusses the problem of modelling linguistic uncertainty, which is the uncertainty produced by statements in natural language. For example, the vague statement `Mary is young' produces uncertainty about Mary's age. We concentrate on simple affirmative statements of the type `subject is pr ..."
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Cited by 16 (3 self)
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The paper discusses the problem of modelling linguistic uncertainty, which is the uncertainty produced by statements in natural language. For example, the vague statement `Mary is young' produces uncertainty about Mary's age. We concentrate on simple affirmative statements of the type `subject is predicate', where the predicate satisfies a special condition called monotonicity. For this case, we model linguistic uncertainty in terms of upper probabilities, which are given a behavioural interpretation as betting rates. Possibility measures and probability measures are special types of upper probability measure. We evaluate Zadeh's suggestion that possibility measures should be used to model linguistic uncertainty and the Bayesian claim that probability measures should be used. Our main conclusion is that, when the predicate is monotonic, possibility measures are appropriate models for linguistic uncertainty. We also discuss several assessment strategies for constructing a numerical model.
2004), Intransitivity and Vagueness
 Proceedings of the Ninth International Conference on Principles of Knowledge Representation and Reasoning (KR
"... There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an ..."
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Cited by 12 (1 self)
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There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox. 1
Neutrosophic Logic  Generalization of the Intuitionistic Fuzzy Logic, To be presented at the
 Special Session on Intuitionistic Fuzzy Sets and Related Concepts, of International EUSFLAT Conference
, 2003
"... In this paper one generalizes the intuitionistic fuzzy logic (IFL) and other logics to neutrosophic logic (NL). The differences between IFL and NL (and the corresponding intuitionistic fuzzy set and neutrosophic set) are: a) Neutrosophic Logic can distinguish between absolute truth (truth in all pos ..."
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Cited by 11 (9 self)
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In this paper one generalizes the intuitionistic fuzzy logic (IFL) and other logics to neutrosophic logic (NL). The differences between IFL and NL (and the corresponding intuitionistic fuzzy set and neutrosophic set) are: a) Neutrosophic Logic can distinguish between absolute truth (truth in all possible worlds, according to Leibniz) and relative truth (truth in at least one world), because NL(absolute truth)=1 + while NL(relative truth)=1. This has application in philosophy (see the neutrosophy). That’s why the unitary standard interval [0, 1] used in IFL has been extended to the unitary nonstandard interval] 0, 1 + [ in NL. Similar distinctions for absolute or relative falsehood, and absolute or relative indeterminacy are allowed in NL. b) In NL there is no restriction on T, I, F other than they are subsets of] 0, 1 + [, thus:
Cycling in proofs and feasibility
 Transactions of the American Mathematical Society
, 1998
"... Abstract. There is a common perception by which small numbers are considered more concrete and large numbers more abstract. A mathematical formalization of this idea was introduced by Parikh (1971) through an inconsistent theory of feasible numbers in which addition and multiplication are as usual b ..."
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Cited by 8 (4 self)
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Abstract. There is a common perception by which small numbers are considered more concrete and large numbers more abstract. A mathematical formalization of this idea was introduced by Parikh (1971) through an inconsistent theory of feasible numbers in which addition and multiplication are as usual but for which some very large number is defined to be not feasible. Parikh shows that sufficiently short proofs in this theory can only prove true statements of arithmetic. We pursue these topics in light of logical flow graphs of proofs (Buss, 1991) and show that Parikh’s lower bound for concrete consistency reflects the presence of cycles in the logical graphs of short proofs of feasibility of large numbers. We discuss two concrete constructions which show the bound to be optimal and bring out the dynamical aspect of formal proofs. For this paper the concept of feasible numbers has two roles, as an idea with its own life and as a vehicle for exploring general principles on the dynamics and geometry of proofs. Cycles can be seen as a measure of how complicated a proof can be. We prove that short proofs must have cycles. 1.
Vagueness and Linguistics
"... An expression is vague, if its meaning is not precise. For vagueness at the sentencelevel this means that a vague sentence does not give rise to precise truth conditions. This is a problem for the standard theory of meaning within linguistics, because this theory presupposes that each sentence has ..."
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Cited by 5 (0 self)
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An expression is vague, if its meaning is not precise. For vagueness at the sentencelevel this means that a vague sentence does not give rise to precise truth conditions. This is a problem for the standard theory of meaning within linguistics, because this theory presupposes that each sentence has a precise
Vagueness as Closeness
 Australasian Journal of Philosophy
, 2005
"... This paper presents and defends a definition of vagueness, compares it favourably with alternative definitions, and draws out some consequences of accepting this definition for the project of offering a substantive theory of vagueness. The definition is roughly this: a predicate ‘F ’ is vague just i ..."
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Cited by 5 (0 self)
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This paper presents and defends a definition of vagueness, compares it favourably with alternative definitions, and draws out some consequences of accepting this definition for the project of offering a substantive theory of vagueness. The definition is roughly this: a predicate ‘F ’ is vague just in case for any objects a and b, ifa and b are very close in respects relevant to the possession of F, then ‘Fa ’ and ‘Fb ’ are very close in respect of truth. The definition is extended to cover vagueness of manyplace predicates, of properties and relations, and of objects. Some of the most important advantages of the definition are that it captures the intuitions which motivate the thought that vague predicates are tolerant, without leading to contradiction, and that it yields a clear understanding of the relationships between higherorder vagueness, sorites susceptibility, blurred boundaries, and borderline cases. The most notable consequence of the definition is that the correct theory of vagueness must countenance degrees of truth. In this paper I present and defend a definition of vagueness, and draw out
Implicit versus explicit comparatives
"... It is natural to assume that the explicit comparative – John is taller than Mary – can be true in cases the implicit comparative – John is tall compared to Mary – is not. This is sometimes seen as a threat to comparisonclass based analyses of the comparative. In this paper it is claimed that the di ..."
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Cited by 3 (3 self)
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It is natural to assume that the explicit comparative – John is taller than Mary – can be true in cases the implicit comparative – John is tall compared to Mary – is not. This is sometimes seen as a threat to comparisonclass based analyses of the comparative. In this paper it is claimed that the distinction between explicit and implicit comparatives corresponds to the difference between (strict) weak orders and semiorders, and that both can be characterized naturally in terms of constraints on the behavior of predicates among different comparison classes.
Learning about the Structure of Scales: Adverbial Modification and the Acquisition of the Semantics of Gradable Adjectives
, 2007
"... This work investigates children’s early semantic representations of gradable adjectives (GAs) and proposes that infants perform a probabilistic analysis of the input to learn about abstract differences within this category. I first demonstrate that children as young as age three distinguish between ..."
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This work investigates children’s early semantic representations of gradable adjectives (GAs) and proposes that infants perform a probabilistic analysis of the input to learn about abstract differences within this category. I first demonstrate that children as young as age three distinguish between relative (e.g., big, long), maximum standard absolute (e.g., full, straight), and minimum standard absolute (e.g., spotted, bumpy) GAs in the way that the standard of comparison is set and how it interacts with the discourse context. I then ask if adverbs enable infants to learn these differences. In a corpus analysis, I demonstrate that statistically significant patterns of adverbial modification are available to the language learner: restricted adverbs (e.g., completely) are more likely than nonrestricted adverbs (e.g., very) to select for maximal GAs with bounded scales. Nonmaximal GAs, which are more likely to be modified by adverbs in general, are more likely to be modified by a narrower range, predominantly composed of intensifiers (e.g., very). I then ask if language learners recruit this information when learning new adjectives. In a word learning task employing the preferential looking paradigm, I demonstrate that 30montholds use adverbial modifiers they are not necessarily producing to assign an interpretation to novel adjectives. Adjectives modified by completely are assigned an
Preserved thematic and impaired taxonomic categorization: A case study
 Language and Cognitive Processes
, 2004
"... case study. ..."