Abstract not found

. 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 mo...

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

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.

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 non-standard 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:

An expression is vague, if its meaning is not precise. For vagueness at the sentence-level 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

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 comparison-class 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 semi-orders, and that both can be characterized naturally in terms of constraints on the behavior of predicates among different comparison classes.

this paper I present and defend a definition of vagueness, and draw out some consequences of accepting this definition. 1 asks what we should properly expect of a definition of vagueness, and 2 reviews existing definitions. 3 explains a key background notion necessary to an understanding of the definition to be presented here. 4 presents this definition, and 5 explains its advantages. 6 draws out the consequences of accepting this definition for the project of offering a substantive theory of vagueness, and 7 considers and rejects a variation on the definition offered here. 1 What should we demand of a definition of vagueness? I take a definition of a property, object or phenomenon P to be a statement about what it is to be P that is true, useful and fundamental

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 non-restricted adverbs (e.g., very) to select for maximal GAs with bounded scales. Non-maximal 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 30-month-olds use adverbial modifiers they are not necessarily producing to assign an interpretation to novel adjectives. Adjectives modified by completely are assigned an

Vagueness is the phenomenon that natural language predicates have borderline regions of applicability and that the boundaries of the borderline region are not determinable. A theory is presented which argues that vagueness is due to the fact that we are computationally bound by Church’s Thesis. Syntactic and semantic models motivated by the theory are introduced. Each disallows the use of classical negation, capturing the fact that it is generally only possible to semidecide but not decide our interpretations of natural language predicates. The role of negation is filled, for each predicate R, by the existence of a dual predicate nonR that acts as if it is the negation, although its interpretation is generally, at best, only an approximation to the complement of R. Multiple “levels ” of vagueness are modeled using concepts from recursion theory.