L o g A G : An algebraic non-monotonic logic for reasoning with graded propositions
- PDF / 2,689,022 Bytes
- 56 Pages / 439.642 x 666.49 pts Page_size
- 66 Downloads / 146 Views
LogA G: An algebraic Non-Monotonic logic for reasoning with graded propositions Nourhan Ehab1 · Haythem O. Ismail1,2
© Springer Nature Switzerland AG 2020
Abstract We present LogA G, a weighted algebraic non-monotonic logic for reasoning with graded beliefs. LogA G is algebraic in that it is a language of only terms, some of which denote propositions and may be associated with ordered grades. The grades could be taken to represent a wide variety of phenomena including preference degrees, priority levels, trust ranks, and uncertainty measures. Reasoning in LogA G is non-monotonic and may give rise to contradictions. Belief revision is, hence, an integral part of reasoning and is guided by the grades. This yields a quite expressive language providing an interesting alternative to the currently existing approaches to non-monotonicity. We show how LogA G can be utilised for modelling resource-bounded reasoning; simulating inconclusive reasoning with circular, liar-like sentences; and reasoning about information arriving over a chain of sources each with a different degree of trust. While there certainly are accounts in the literature for each of these issues, we are not aware of any single framework that accounts for them all like LogA G does. We also show how LogA G captures a wide variety of non-monotonic logical formalisms. As such, LogA G is a unifying framework for non-monotonicity which is flexible enough to admit a wide array of potential uses. Keywords Non-Monotonicity · Weighted logics · Uncertainty · Graded propositions · Unified framework for Non-Monotonicity Mathematics Subject Classification (2010) 68T27
1 Introduction Most of the commonsense reasoning we perform in our everyday lives typically involves uncertain, possibly contradicting, beliefs. Consequently, any intelligent agent emulating Nourhan Ehab
[email protected] Haythem O. Ismail [email protected] 1
Department of Computer Science and Engineering, German University in Cairo, Cairo, Egypt
2
Department of Engineering Mathematics, Cairo University, Giza, Egypt
N. Ehab, H. O. Ismail
human reasoning must be able to handle uncertain knowledge in a way that facilitates drawing reasonable conclusions, and resolve contradictions when they arise. The uncertainty in the available information can manifest itself in various forms: (1) the information obtained may only be partial, in that answers to several questions are not known; (2) the available information may be approximate, in that all the required answers are known but they are not totally accurate or reliable; or (3) the information obtained from the knowledge sources could be inconsistent. A common approach to handle all the above forms of uncertainty is non-monotonicity. Modelling non-monotonicity has been the focus of extensive studies in the knowledge representation and reasoning community for many years giving rise to a vast family of non-monotonic formalisms. The work presented in this paper is one attempt. We present an algebraic non-monotonic logic we refer to as LogA G f
Data Loading...
