General Theory Of Computation Research Articles

Toward a comprehensive theory of emotion for biological and artificial agents

Abstract A new model of emotions that is applicable to both biological and artificial agents is proposed. The description includes theoretical foundations, internal representation, and the role of emotions in cognition. This model is based on definitions of emotions in valence and arousal space coupled with an adaptation of Maslow’s hierarchy and other ideas. The resulting architecture provides for a significantly more expressive range and organization of represented emotional experience compared to other models. Requirements for a satisfactory general computational theory of emotions are applied to the new theory and analyzed in terms of (i) neurological and psychological plausibility, (ii) range and complexity of human emotional experience, (iii) applicability to learning, memory, behavior, and decision-making, and (iv) consistency with well-accepted models and general facts about emotions. The model is implemented and studied through simulations of virtual agent-based systems. Presented results support the model’s applicability to perception, action selection, learning, and memory in virtual agents capable of human-like behavior. Paradigms and predictions allowing for further validation of the new model and emotion theories in general are discussed.

The foundations of computation, physics and mentality: the Turing legacy

The foundations of computation, physics and mentality: the Turing legacy

Logically Possible Machines

I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). There are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds.

Rotation function for integrable problems reducing to the Abel equations. Orbital classification of Goryachev-Chaplygin systems.

The rotation vector, one of the most important orbital invariants of integrable Hamiltonian systems with two degrees of freedom, is constructed using the rotation function (see [1]). A general theory of computation of the rotation functions for dynamical systems reducing to the Abel equations is developed. Using this theory, an explicit formula for the rotation function in the Goryachev-Chaplygin case in the dynamics of heavy rigid bodies is obtained. The orbital classification of the family of Goryachev-Chaplygin systems for different values of energy is presented. For this purpose the orbital Fomenko-Bolsinov invariant, which is the classifying object, is computed. The orbital non-equivalence of the Goryachev-Chaplygin flows on surfaces of equal energy corresponding to different energy levels is established as a result of an analytic study and computer analysis (together with S. Takahasi, Japan) . In addition, explicit formulae for the transition from the coordinate system on the Jacobian (the Abelian variables) to the Euler-Poisson coordinate system in the Goryachev-Chaplygin case are obtained and the covering of the Jacobian by the Liouville torus is studied. This can be used for finding an explicit solution to the Goryachev-Chaplygin problem in terms of two-dimensional theta functions.

A universal cellular automaton in quasi-linear time and its S—m—n form

In this paper, we describe a quasi-linear time universal cellular automaton. This cellular automaton is not only computation universal (in the sense of simulating any Turing machine), but also intrinsically universal (it is capable of simulating arbitrary one-dimensional cellular automata, even two-way). The simulation is based on a novel programming language (the brick language), which simplifies the recursive specifications of transition functions. Moreover, we prove that cellular automata form an acceptable programming system for parallel computation, thus providing an S-m-n theorem for cellular automata. This allows us to apply well-known results of the general theory of computation to cellular automata and might give a practical framework for studying the structural complexity of cellular automata computations.

A model of comparative stylistics for machine translation

The study of comparative stylistics attempts to catalogue and explain the differences in style between languages. Rules of comparative stylistics are commonly presented in textbooks of translation as simple ‘rules of thumb’, but if we hope to incorporate a knowledge of comparative stylistics into machine translation systems, we must take a more systematic approach. We develop a formal model of comparative syntactic stylistics to be used as a component of a general computational theory of style. We adapt textbook rules of human translation and study a small corpus of French-English translations to determine how these informal rules can be represented in our model as formal rules of translation. Our model of comparative stylistics could be implemented in a machine translation system, enabling the system to make a more informed decision about possible translation choices and their potential stylistic effects.

Functional models of neurobiological processes

This paper uses a very general theory of computation to develop a set of working hypotheses and an accompanying mathematical formalism that model the semantics and structure of cognitive processes. We can think of the brain as a modular system of neural networks, each producing a sequence of output states in response to input states furnished by others, and sometimes by the outside world. We use category theory to specify, and reason about, a model consisting of an appropriately connected set of functions.