Narrow Results

In this paper, we would like to present some logics with semantics based on rough set theory and related notions. These logics are mainly divided into two classes. One is the class of modal logics and the other is that of quantifier logics. For the former, the approximation space is based on a set of possible worlds, whereas in the latter, we consider the set of variable assignments as the universe of approximation. In addition to surveying some well-known results about the links between logics and rough set notions, we also develop some new applied logics inspired by rough set theory.

Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as processes of learning which change game models. Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. This dynamic stance provides a new look at the current interface of games, logic, and computation.

Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as processes of learning which change game models. Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. This dynamic stance provides a new look at the current interface of games, logic, and computation.

We study the applicability of declarative models to encode and describe structured information by means of semantics. Specifically, we introduce D-SPACES, an implementation of constraint systems with space and extrusion operators. Constraint systems are algebraic models that allow for a semantic language-like representation of information in systems where the concept of space is a primary structural feature. We mainly give this information an epistemic or temporal interpretation and consider various agents as entities acting upon it. D-SPACES is coded as a c++ library providing implementations of constraint systems, space functions and extrusion functions. The interfaces to access each implementation are minimal and thoroughly documented. D-SPACES also provides property-checking methods as well as an implementation of a specific type of constraint systems (a boolean algebra). This last implementation serves as an entry point for quick access and proof of concept when using these models. Finally, we show the applicability of this framework with two examples; a scenario in the form of a social network where users post their beliefs and utter their opinions, and a semantical interpretation of a logical language to express time behaviors and properties.

I propose a class of TW-models for epistemic logic, Kripke's models in character with reexivity as the only constraint on the required accessibility relation amongst states, which will satisfy the main theses of Timothy Williamson's knowledge first epistemology. I introduce a function δ from the set S of states to the power set of formulae of the language in use, referred to as ipk-function to signify Williamso's notion of ‘the agent's being in a position to know a proposition in a state’. The semantic rules for the modal operators (for ‘knowing’) and (for ‘believing’) will be stipulated, respectively. The proposed semantic rules not only illuminate Williamson's thesis of understanding the justification of belief in terms of knowledge but also illustrate that to construct models for an epistemic logic with both knowledge-operator and belief-operator , we need not posit two distinct accessibility relations for and respectively. Moreover, TW-models will invalidate a list of problematic formulae/rules of inference, which are taken as the characterization of the problem of logical omniscience. Finally, I add to the original language one extra operator (corresponding to the ipk-function in that , meaning ‘the agent being actually in a position to know φ’, is true in a state α if and only if φ ∈ τ(α)), so that the derivability-power of the problematic formulae/rules of inference can be retained in the desired epistemic logic system by corresponding modified formulae.