7110538
Only Persistence Makes Nonmonotonicity Monotonous
An important characteristic of many logics for artificial intelligence is that they are nonmonotonic. This means that adding a formula to the premises can destroy some of the consequences. There may exist formulae that can always be safely added to the premises without destroying any of the consequences: they respect monotonicity. We consider three preferential logics for which we analyze the class of formulae which respect monotonicity. For each of the three logics we show that this class is equal to the class of formulae preserved under going to more preferred models, and we provide syntactic characterizations of these classes.
9865419
A compositional reasoning system for executing nonmonotonic theories of reasoning
In this paper the framework DESIRE for the design of compositional reasoning systems and multi-agent systems was applied to build a generic nonmonotonic reasoning system. The outcome is a general reasoning system that can be used to model different nonmonotonic reasoning formalisms and that can be executed by a generic execution mechanism. The main advantages of using DESIRE (for example, compared to a direct implementation in a programming language such as PROLOG) are that the design is generic and has a transparent compositional structure, and the explicit declarative specification of both the static and dynamic aspects of the nonmonotonic reasoning processes, including their control. © 2003 Wiley Periodicals, Inc.
34555418
Nonmonotonic Reasoning with Multiple Belief Sets
In the present paper we introduce nonmonotonic belief set operators and selection operators to formalize and to analyze multiple belief sets in an abstract setting. We define and investigate formal properties of belief set operators as absorption, congruence, supradeductivity and weak belief monotony. Furthermore, it is shown that for each belief set operator satisfying strong belief cumulativity there exists a largest monotonic logic underlying it, thus generalizing a result for nonmonotonic inference operations. Finally, we study abstract properties of selective inference operations connected to belief set operators and which are used to choose one of the possible views.
32078047
Temporal Theories of Reasoning
In this paper we describe a general way of formalizing reasoning behaviour. Such a behaviour may be described by all the patterns which are valid for the behaviour. A pattern can be seen as a sequence of information states which describe what has been derived at each time point. A transition from an information state at a point in time to the state at the (or a) next time point is induced by one or more inference steps. We choose to model the information states by partial models and the patterns either by linear time or branching time temporal models. Using temporal logic one can define theories and look at all models of that theory. For a number of examples of reasoning behaviour we have been able to define temporal theories such that its (minimal) models correspond to the valid patterns of the behaviour. These theories prescribe that the inference steps which are possible, are "executed" in the temporal model. The examples indicate that partial temporal logic is a powerful means of describing and formalizing complex reasoning patterns, as the dynamic aspects of reasoning systems are integrated into the static ones in a clear fashion.
40535872
Compositional Verification of Multi-Agent Systems in Temporal Multi-Epistemic Logic
Compositional verification aims at managing the complexity of theverification process by exploiting compositionality of the systemarchitecture. In this paper we explore the use of a temporal epistemiclogic to formalize the process of verification of compositionalmulti-agent systems. The specification of a system, its properties andtheir proofs are of a compositional nature, and are formalized within acompositional temporal logic: Temporal Multi-Epistemic Logic. It isshown that compositional proofs are valid under certain conditions.Moreover, the possibility of incorporating default persistence ofinformation in a system, is explored. A completion operation on aspecific type of temporal theories, temporal completion, is introducedto be able to use classical proof techniques in verification withrespect to non-classical semantics covering default persistence.
1862248
Monotonicity and Persistence in Preferential Logics
An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be safely added to the premises without destroying any of the consequences: we say they respect monotonicity. Also, there may be formulae that, when they are a consequence, can not be invalidated when adding any formula to the premises: we call them conservative. We study these two classes of formulae for preferential logics, and show that they are closely linked to the formulae whose truth-value is preserved along the (preferential) ordering. We will consider some preferential logics for illustration, and prove syntactic characterization results for them. The results in this paper may improve the efficiency of theorem provers for preferential logics.
17757601
A Kleene characterization of computability
The recursively enumerable binary relations are the smallest class containing all singleton relations and closed under union, concatenation, Kleene star, composition, and transitive closure.
17560850
Clique-Width for Four-Vertex Forbidden Subgraphs
Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms. The notion of clique-width extends the one of treewidth, since bounded treewidth implies bounded clique-width. We give a complete classification of all graph classes defined by forbidden induced subgraphs of at most four vertices with respect to bounded or unbounded clique-width.
47462408
The equivalence problem for deterministic MSO tree transducers is decidable
It is decidable for deterministic MSO definable graph-to-string or graph-to-tree transducers whether they are equivalent on a context-free set of graphs.
20050455
Clique-Width for 4-Vertex Forbidden Subgraphs
Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms. The notion of clique-width extends the one of treewidth, since bounded treewidth implies bounded clique-width. We give a complete classification of all graph classes defined by forbidden induced subgraphs of at most four vertices with respect to bounded or unbounded clique-width.
9307461
Context Free Normal Systems and ETOL Systems
Abstract The relationship between extended context free normal systems (a nondeterministic version of Tag systems of Post with deletion number equal to 1 and using nonterminals) and ETOL systems is considered. It is demonstrated that the class of languages generated by context free normal systems (denoted L (ECFN)) lies strictly between the clas of EOL languages (denoted L (EOL)) and the class of ETOL languages. Several characterizations of L (ECFN)) in terms of L (EOL)) are provided and a number of closure properties of L '(ECFN) are established.