Modeling of Phenomena and Dynamic Logic of Phenomena

Modeling of complex phenomena such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, problem or theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models

Tractability and the computational mind

We overview logical and computational explanations of the notion of tractability as applied in cognitive science. We start by introducing the basics of mathematical theories of complexity: computability theory, computational complexity theory, and descriptive complexity theory. Computational philosophy of mind often identifies mental algorithms with computable functions. However, with the development of programming practice it has become apparent that for some computable problems finding effective algorithms is hardly possible. Some problems need too much computational resource, e.g., time or memory, to be practically computable. Computational complexity theory is concerned with the amount of resources required for the execution of algorithms and, hence, the inherent difficulty of computational problems. An important goal of computational complexity theory is to categorize computational problems via complexity classes, and in particular, to identify efficiently solvable problems and draw a line between tractability and intractability. We survey how complexity can be used to study computational plausibility of cognitive theories. We especially emphasize methodological and mathematical assumptions behind applying complexity theory in cognitive science. We pay special attention to the examples of applying logical and computational complexity toolbox in different domains of cognitive science. We focus mostly on theoretical and experimental research in psycholinguistics and social cognition

Playing to Learn, or to Keep Secret: Alternating-Time Logic Meets Information Theory

Many important properties of multi-agent systems refer to the participants' ability to achieve a given goal, or to prevent the system from an undesirable event. Among intelligent agents, the goals are often of epistemic nature, i.e., concern the ability to obtain knowledge about an important fact \phi. Such properties can be e.g. expressed in ATLK, that is, alternating-time temporal logic ATL extended with epistemic operators. In many realistic scenarios, however, players do not need to fully learn the truth value of \phi. They may be almost as well off by gaining some knowledge; in other words, by reducing their uncertainty about \phi. Similarly, in order to keep \phi secret, it is often insufficient that the intruder never fully learns its truth value. Instead, one needs to require that his uncertainty about \phi never drops below a reasonable threshold. With this motivation in mind, we introduce the logic ATLH, extending ATL with quantitative modalities based on the Hartley measure of uncertainty. The new logic enables to specify agents' abilities w.r.t. the uncertainty of a given player about a given set of statements. It turns out that ATLH has the same expressivity and model checking complexity as ATLK. However, the new logic is exponentially more succinct than ATLK, which is the main technical result of this paper

Logical models for bounded reasoners

This dissertation aims at the logical modelling of aspects of human reasoning, informed by facts on the bounds of human cognition. We break down this challenge into three parts. In Part I, we discuss the place of logical systems for knowledge and belief in the Rationality Debate and we argue for systems that formalize an alternative picture of rationality -- one wherein empirical facts have a key role (Chapter 2). In Part II, we design logical models that encode explicitly the deductive reasoning of a single bounded agent and the variety of processes underlying it. This is achieved through the introduction of a dynamic, resource-sensitive, impossible-worlds semantics (Chapter 3). We then show that this type of semantics can be combined with plausibility models (Chapter 4) and that it can be instrumental in modelling the logical aspects of System 1 (“fast”) and System 2 (“slow”) cognitive processes (Chapter 5). In Part III, we move from single- to multi-agent frameworks. This unfolds in three directions: (a) the formation of beliefs about others (e.g. due to observation, memory, and communication), (b) the manipulation of beliefs (e.g. via acts of reasoning about oneself and others), and (c) the effect of the above on group reasoning. These questions are addressed, respectively, in Chapters 6, 7, and 8. We finally discuss directions for future work and we reflect on the contribution of the thesis as a whole (Chapter 9)

09351 Abstracts Collection -- Information processing, rational belief change and social interaction

From 23.08. to 27.08.2009, the Dagstuhl Seminar 09351 ``Information processing, rational belief change and social interaction \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available