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.
17644062
Specification of nonmonotonic reasoning
ABSTRACT Two levels of description of nonmonotonic reasoning are distinguished. For these levels semantical formalizations are given. The first level is defined semantically by the notion of belief state frame, the second level by the notion of reasoning frame. We introduce two specification languages to describe nonmonotonic reasoning at each of the levels: (1) a specification language for level 1, with formal semantics based on belief state frames, (2) a fragment of infinitary temporal logic as a general specification language for level 2, with formal semantics based on reasoning frames. In our framework every level 2 description can be abstracted to level 1, and for every level 1 description there are level 2 descriptions which are a specialization of it.
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.
41515310
Minimal Temporal Epistemic Logic
35737768
A Compositional Reasoning System for Executing Nonmonotonic Theories of Reasoning
In this paper a system was developed using the compositional modelling environment DESIRE (framework for DEsign and Specification of Interacting REasoning components). This environment for the development of compositional reasoning systems and multi-agent systems has been succesfully used to design various types of reasoning systems and multi-agent systems and applications in particular domains. The DESIRE sofware environment offers a graphical editor, an implementation generator and an execution environment to execute specifications automatically.
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.
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.
14472583
An exercise in structural congruence
Milner's structural congruence is decidable for the pi-calculus without restriction, in exponential space.
11417476
Look-Ahead on Pushdowns
Abstract The general notion of look-ahead on pushdowns is used to prove that (1) the deterministic iterated pushdown languages are closed under complementation, (2) the deterministic iterated pushdown languages are properly included in the non-deterministic iterated pushdown languages; the counter example is a very simple linear context-free language, independent of the amount of iteration, (3) LL ( k ) iterated indexed grammars can be parsed by deterministic iterated pushdown automata, and (4) it is decidable whether an iterated indexed grammar is LL ( k ). Analogous results hold for iterated pushdown automata with regular look-ahead on the input, and LL -regular iterated indexed grammars.
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.
17739753
Finite Languages for the Representation of Finite Graphs
We introduce a new way of specifying graphs: through languages, i.e., sets of strings. The strings of a given (finite, prefix-free) language represent the vertices of the graph; whether or not there is an edge between the vertices represented by two strings is determined by the pair of symbols at the first position in these strings where they differ. With this new, “positional” or lexicographic, method, classical and well-understood ways of specifying languages can now be used to specify graphs, in a compact way; thus, (small) finite automata can be used to specify (large) graphs. Since (prefix-free) languages can be viewed as trees, our method generalizes the hierarchical specification of particular types of graphs such as cographs and VSP graphs. Our main results demonstrate an intrinsic relationship between the fundamental operations of language concatenation and graph substitution.