A Propositional Dynamic Logic Approach for Order of Magnitude Reasoning
نویسندگان
چکیده
We introduce a Propositional Dynamic Logic for order of magnitude reasoning in order to formalize qualitative operations of sum and product. This new logic has enough expressive power to consider, for example, the concept of closeness, and to study some interesting properties for the qualitative operations, together with the logical definability of these properties. Finally, we show the applicability of our approach on the basis of some examples.
منابع مشابه
Relational approach for a logic for order of magnitude qualitative reasoning with negligibility, non-closeness and distance
We present a relational proof system in the style of dual tableaux for a multimodal propositional logic for order of magnitude qualitative reasoning to deal with relations of negligibility, non-closeness, and distance. This logic enables us to introduce the operation of qualitative sum for some classes of numbers. A relational formalization of the modal logic in question is introduced in this p...
متن کاملCloseness and Distance Relations in Order of Magnitude Qualitative Reasoning via PDL
The syntax, semantics and an axiom system for an extension of Propositional Dynamic Logic (PDL) for order of magnitude qualitative reasoning which formalizes the concepts of closeness and distance is introduced in this paper. In doing this, we use some of the advantages of PDL: firstly, we exploit the possibility of constructing complex relations from simpler ones for defining the concept of cl...
متن کاملDual tableau for a multimodal logic for order of magnitude qualitative reasoning with bidirectional negligibility
The use of models to represent different scientific and engineering situations leads to qualitative reasoning as a good possibility when the traditional numerical methods are limited. Qualitative Reasoning (QR) provides an intermediate level between discrete and continuous models. A form of QR is to manage numerical data in terms of orders of magnitude (see, for example, [12, 14]). Two approach...
متن کاملReasoning about Actions with Temporal Answer Sets
In this paper we define a Temporal Action Theory through a combination of Answer Set Programming and Dynamic Linear Time Temporal Logic (DLTL). DLTL extends propositional temporal logic of linear time with regular programs of propositional dynamic logic, which are used for indexing temporal modalities. In our language, general temporal constraints can be included in domain descriptions. We defi...
متن کاملEquality propositional logic and its extensions
We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...
متن کامل