Languages for Gestalts of line patterns

Any formal model of visual Gestalt perception requires a language for representing possible perceptual structures of visual stimuli, as well as a decision criterion that selects the actually perceived structure of a stimulus among its possible alternatives. This paper discusses an existing model of visual Gestalt perception that is based on Structural Information Theory. We investigate two factors that determine the representational power of this model: the domain of visual stimuli that can be analyzed, and the class of perceptual structures that can be generated for these stimuli. We show that the representational power of the existing model of Structural Information Theory is limited, and that some of the generated structures are perceptually inadequate. We argue that these limitations do not imply the implausibility of the underlying ideas of Structural Information Theory and introduce alternative models based on the same ideas. For each of these models, the domain of visual stimuli that can be analyzed properly is formally defined. We show that the models are conservative modifications of the original model of Structural Information Theory: for cases that are adequately analyzed in the original model of Structural Information Theory, they yield the same results.     

Languages and designs for probability judgment

Theories of subjective probability are viewed as formal languages for analyzing evidence and expressing degrees of belief. This article focuses on two probability langauges, the Bayesian language and the language of belief functions (Shafer, 1976). We describe and compare the semantics (i.e., the meaning of the scale) and the syntax (i.e., the formal calculus) of these languages. We also investigate some of the designs for probability judgment afforded by the two languages.     

Logic,Logic, and Logic

In his recent paper in History and Philosophy of Logic, John Kearns argues for a solution of the Liar paradox using an illocutionary logic (Kearns 2007 Kearns, J. 2007. ‘An illocutionary logical explanation of the Liar Paradox’. History and Philosophy of Logic, 28: 31–66. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Paraconsistent approaches, especially dialetheism, which accepts the Liar as being both true and false, are rejected by Kearns as making no ‘clear sense’ (p. 51). In this critical note, I want to highlight some shortcomings of Kearns' approach that concern a general difficulty for supposed solutions to (semantic) antinomies like the Liar. It is not controversial that there are languages which avoid the Liar. For example, the language which consists of the single sentence ‘Benedict XVI was born in Germany’ lacks the resources to talk about semantics at all and thus avoids the Liar. Similarly, more interesting languages such as the propositional calculus avoid the Liar by lacking the power to express semantic concepts or to quantify over propositions. Kearns also agrees with the dialetheist claim that natural languages are semantically closed (i.e. are able to talk about their sentences and the semantic concepts and distinctions they employ). Without semantic closure, the Liar would be no real problem for us (speakers of natural languages). But given the claim, the expressive power of natural languages may lead to the semantic antinomies. The dialetheist argues for his position by proposing a general hypothesis (cf. Bremer 2005 Bremer, M. 2005. An Introduction to Paraconsistent Logics, Bern: Lang.  [Google Scholar], pp. 27–28): ‘(Dilemma) A linguistic framework that solves some antinomies and is able to express its linguistic resources is confronted with strengthened versions of the antinomies’. Thus, the dialetheist claims that either some semantic concepts used in a supposed solution to a semantic antinomy are inexpressible in the framework used (and so, in view of the claim, violate the aim of being a model of natural language), or else old antinomies are exchanged for new ones. One horn of the dilemma is having inexpressible semantic properties. The other is having strengthened versions of the antinomies, once all semantic properties used are expressible. This dilemma applies, I claim, to Kearns' approach as well.     

Logic for physical space

Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major milestones in the logical representation of space and investigate current trends. In doing so, we do not only consider classical logic, but we indulge ourselves with modal logics. These present themselves naturally by providing simple axiomatizations of different geometries, topologies, space-time causality, and vector spaces.     

Generating Facial Expressions for Speech

This article reports results from a program that produces high-quality animation of facial expressions and head movements as automatically as possible in conjunction with meaning-based speech synthesis, including spoken intonation. The goal of the research is as much to test and define our theories of the formal semantics for such gestures, as to produce convincing animation. Towards this end, we have produced a high-level programming language for three-dimensional (3-D) animation of facial expressions. We have been concerned primarily with expressions conveying information correlated with the intonation of the voice: This includes the differences of timing, pitch, and emphasis that are related to such semantic distinctions of discourse as “focus,”“topic,” and “comment,”“theme” and “rheme,” or “given” and “new” information. We are also interested in the relation of affect or emotion to facial expression. Until now, systems have not embodied such rule-governed translation from spoken utterance meaning to facial expressions. Our system embodies rules that describe and coordinate these relations: intonation/information, intonation/affect, and facial expressions/affect. A meaning representation includes discourse information: What is contrastive/background information in the given context, and what is the “topic” or “theme” of the discourse? The system maps the meaning representation into how accents and their placement are chosen, how they are conveyed over facial expression, and how speech and facial expressions are coordinated. This determines a sequence of functional groups: lip shapes, conversational signals, punctuators, regulators, and manipulators. Our algorithms then impose synchrony, create coarticulation effects, and determine affectual signals, eye and head movements. The lowest level representation is the Facial Action Coding System (FACS), which makes the generation system portable to other facial models.     

Logic for dialogue games

The purpose of this paper is to work toward an explicit logic and semantics for a game theoretically inspired theory of action. The purpose of the logic is to explicate the conceptual machinery implicit in the dialogue-game model of rational discourse developed in Carlson (1983).A variety of ideas and techniques of modal and philosophical logic are used to define a model structure that generalizes the game theoretical notion of a game in extensive form (von Neumann and Morgenstern, 1944). Relative to this model structure, semantic characterizations are given to the action-theoretic notions oftime, possibility, belief, preference, ability, intention, action, andrationality. The unification of these characterizations under the game-theoretical paradigm leads to insights about the logical interdependences between these concepts.The resulting theory of rational interaction is applied to the explication of rational dialogue. The main benefit of the enterprise for a theory of rational dialogue is that concepts and results of game theory become accessible to the explication of dialogue. In particular, the task of proving the logical coherence of a discourse is reduced to the task of showing the rationality of strategy choices made in an associated dialogue game.     

Proto-Semantics for Positive Free Logic

This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of non-existing objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth non unlike the notion of truth at world found in modal logic. A model theory is developed, establishing compactness, interpolation (implying a strong form of Beth definability), and completeness (with respect to a particular axiomatization).     

A Temporal Logic for Sortals

With the past and future tense propositional operators in its syntax, a formal logical system for sortal quantifiers, sortal identity and (second order) quantification over sortal concepts is formulated. A completeness proof for the system is constructed and its absolute consistency proved. The completeness proof is given relative to a notion of logical validity provided by an intensional semantic system, which assumes an approach to sortals from a modern form of conceptualism.     

A Logic for Information Systems

A conception of an information system has been introduced by Pawlak. The study has been continued in works of Pawlak and Orlowska and in works of Vakarelov. They had proposed some basic relations and had constructed a formal system of a modal logic that describes the relations and some of their Boolean combinations. Our work is devoted to a generalization of this approach. A class of relation systems and a complete calculus construction method for these systems are proposed. As a corollary of our main result, our paper contains a solution of a Vakarelov's problem: how to construct a formal system that describes all the Boolean combinations of the basic relations.     

Natural Deduction for Dual-intuitionistic Logic

We present a natural deduction system for dual-intuitionistic logic. Its distinctive feature is that it is a single-premise multiple-conclusions system. Its relationships with the natural deduction systems for intuitionistic and classical logic are discussed.     

A Logic for Disjunctive Ignorance

In this paper, we introduce a notion of ‘disjunctive ignorance’, which is a weak combination of two forms of ignorance in the literature. We propose a logical language with ‘disjunctive ignorance’ as a sole modality, explore the logical properties of this notion and its related notions, and axiomatize it over various frame classes. By finding suitable reduction axioms, we extend the results to the case of public announcements and apply it to Moore-like sentences.