Typicality, graded membership, and vagueness

This paper addresses theoretical problems arising from the vagueness of language terms, and intuitions of the vagueness of the concepts to which they refer. It is argued that the central intuitions of prototype theory are sufficient to account for both typicality phenomena and psychological intuitions about degrees of membership in vaguely defined classes. The first section explains the importance of the relation between degrees of membership and typicality (or goodness of example) in conceptual categorization. The second and third section address arguments advanced by Osherson and Smith (1997), and Kamp and Partee (1995), that the two notions of degree of membership and typicality must relate to fundamentally different aspects of conceptual representations. A version of prototype theory—the Threshold Model—is proposed to counter these arguments and three possible solutions to the problems of logical selfcontradiction and tautology for vague categorizations are outlined. In the final section graded membership is related to the social construction of conceptual boundaries maintained through language use

Linear Time Logics - A Coalgebraic Perspective

We describe a general approach to deriving linear time logics for a wide variety of state-based, quantitative systems, by modelling the latter as coalgebras whose type incorporates both branching behaviour and linear behaviour. Concretely, we define logics whose syntax is determined by the choice of linear behaviour and whose domain of truth values is determined by the choice of branching, and we provide two equivalent semantics for them: a step-wise semantics amenable to automata-based verification, and a path-based semantics akin to those of standard linear time logics. We also provide a semantic characterisation of the associated notion of logical equivalence, and relate it to previously-defined maximal trace semantics for such systems. Instances of our logics support reasoning about the possibility, likelihood or minimal cost of exhibiting a given linear time property. We conclude with a generalisation of the logics, dual in spirit to logics with discounting, which increases their practical appeal in the context of resource-aware computation by incorporating a notion of offsetting.Comment: Major revision of previous version: Sections 4 and 5 generalise the results in the previous version, with new proofs; Section 6 contains new result

Linguistic classification: T-norms, fuzzy distances and fuzzy distinguishabilities

Abstract Back in 1967 the linguist Ž. Muljacic used an additive distance between ill-defined linguistic features which is a forerunner of the fuzzy Hamming distance between strings of truth values in standard fuzzy logic. Here we show that if the logical frame is changed one obtains additive distances which are either sorely inadequate, as in the Łukasiewicz or probabilistic case, or coincide with the distance originally envisaged by Muljacic, as happens with a whole class of T-norms (abstract logical conjunctions) which includes the nilpotent minimum. All this strengthens the role of Muljacic distances in linguistic clustering and of Muljacic distinguishabilities (a notion subtly different from distances, but quite inalienable) in linguistic evolution. As a preliminary example we re-take and re-examine Muljacic original data

Thinking intuitively: the rich (and at times illogical) world of concepts

Intuitive knowledge of the world involves knowing what kinds of things have which properties. We express it in generalities such as “ducks lay eggs”. It contrasts with extensional knowledge about actual individuals in the world, which we express in quantified statements such as “All US Presidents are male”. Reasoning based on this intuitive knowledge, while highly fluent and plausible may in fact lead us into logical fallacy. Several lines of research point to our conceptual memory as the source of this logical failure. We represent concepts with prototypical properties, judging likelihood and argument strength on the basis of similarity between ideas. Evidence that our minds represent the world in this intuitive way can be seen in a range of phenomena, including how people interpret logical connectives applied to everyday concepts, studies of creativity and emergence in conceptual combination, and demonstrations of the logically inconsistent beliefs that people express in their everyday language

Outline of a Theory of Strongly Semantic Information

Peer reviewe

A map of dependencies among three-valued logics

International audienceThree-valued logics arise in several fields of computer science, both inspired by concrete problems (such as in the management of the null value in databases) and theoretical considerations. Several three-valued logics have been defined. They differ by their choice of basic connectives, hence also from a syntactic and proof-theoretic point of view. Different interpretations of the third truth value have also been suggested. They often carry an epistemic flavor. In this work, relationships between logical connectives on three-valued functions are explored. Existing theorems of functional completeness have laid bare some of these links, based on specific connectives. However we try to draw a map of such relationships between conjunctions, negations and implications that extend Boolean ones. It turns out that all reasonable connectives can be defined from a few of them and so all known three-valued logics appear as a fragment of only one logic. These results can be instrumental when choosing, for each application context, the appropriate fragment where the basic connectives make full sense, based on the appropriate meaning of the third truth-value