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28
An Abstract, ArgumentationTheoretic Approach to Default Reasoning
, 1997
"... We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, nonmonotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a generalisation of Theorist. The generali ..."
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Cited by 162 (23 self)
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We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, nonmonotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a generalisation of Theorist. The generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions. An assumption can be defeated (or "attacked") if its "contrary" can be proved, possibly with the aid of other conflicting assumptions. We show that, given such a framework, the standard semantics of most logics for default reasoning can be understood as sanctioning a set of assumptions, as an extension of a given theory, if and only if the set of assumptions is conflictfree (in the sense that it does not attack itself) and it attacks every assumption not in the set. We propose a more liberal, argumentationtheoretic semantics, based upon the notion of admissible extension in logic pro...
Timed Default Concurrent Constraint Programming
 Journal of Symbolic Computation
, 1996
"... Synchronous programming (Berry (1989)) is a powerful approach to programming reactive systems. Following the idea that "processes are relations extended over time" (Abramsky (1993)), we propose a simple but powerful model for timed, determinate computation, extending the closureoperator model for u ..."
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Cited by 62 (11 self)
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Synchronous programming (Berry (1989)) is a powerful approach to programming reactive systems. Following the idea that "processes are relations extended over time" (Abramsky (1993)), we propose a simple but powerful model for timed, determinate computation, extending the closureoperator model for untimed concurrent constraint programming (CCP). In (Saraswat et al. 1994a) we had proposed a model for this called tcc here we extend the model of tcc to express strong timeouts: if an event A does not happen through time t, cause event B to happen at time t. Such constructs arise naturally in practice (e.g. in modeling transistors) and are supported in synchronous programming languages. The fundamental conceptual difficulty posed by these operations is that they are nonmonotonic. We provide a compositional semantics to the nonmonotonic version of concurrent constraint programming (Default cc) obtained by changing the underlying logic from intuitionistic logic to Reiter's default logic...
Mixed Integer Programming Methods for Computing Nonmonotonic Deductive Databases
, 1994
"... Though the declarative semantics of both explicit and nonmonotonic negation in logic programs has been studied extensively, relatively little work has been done on computation and implementation of these semantics. In this paper, we study three different approaches to computing stable models of logi ..."
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Cited by 45 (8 self)
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Though the declarative semantics of both explicit and nonmonotonic negation in logic programs has been studied extensively, relatively little work has been done on computation and implementation of these semantics. In this paper, we study three different approaches to computing stable models of logic programs based on mixed integer linear programming methods for automated deduction introduced by R. Jeroslow. We subsequently discuss the relative efficiency of these algorithms. The results of experiments with a prototype compiler implemented by us tend to confirm our theoretical discussion. In contrast to resolution, the mixed integer programming methodology is both fully declarative and handles reuse of old computations gracefully. We also introduce, compare, implement, and experiment with linear constraints corresponding to four semantics for "explicit" negation in logic programs: the fourvalued annotated semantics [3], the GelfondLifschitz semantics [12], the overdetermined models ...
The Stable Models of a Predicate Logic Program
 Journal of Logic Programming
, 1992
"... this paper we investigate and solve the problem classifying the Turing complexity of stable models of finite and recursive predicate logic programs. GelfondLifschitz [7] introduced the concept of a stable model M of a Predicate Logic Program P . Here we show that, up to a recursive 11 coding, the ..."
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Cited by 35 (13 self)
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this paper we investigate and solve the problem classifying the Turing complexity of stable models of finite and recursive predicate logic programs. GelfondLifschitz [7] introduced the concept of a stable model M of a Predicate Logic Program P . Here we show that, up to a recursive 11 coding, the set of all stable models of finite Predicate Logic Programs and the 5
Revision Specifications by Means of Programs
 JELIA '94, volume 838 of LNAI
, 1994
"... . We propose a formalism for specifying revisions in knowledge bases and belief sets. This formalism extends logic programming with stable model semantics. Main objects of our system are revision programs consisting of revision rules. A revision rule expresses a specification of change or a constra ..."
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Cited by 20 (0 self)
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. We propose a formalism for specifying revisions in knowledge bases and belief sets. This formalism extends logic programming with stable model semantics. Main objects of our system are revision programs consisting of revision rules. A revision rule expresses a specification of change or a constraint on a knowledge base. There are two types of revision rules. Inrules require that an element be in a knowledge base whenever some other elements are in the knowledge base and yet other elements are absent from it. Similar conditions in an outrule force the absence of an element from the knowledge base. For a revision program P we introduce the notion of a P justified revision, which we use to specify the meaning of the program. Main motivation for our formalism and for the semantics of P justified revisions comes from default logic and logic programming with stable model semantics. In the paper, we show that if a knowledge base B is a model of a program P then B is the unique P ju...
Logical Constraints and Logic Programming
"... In this note we will investigate a form of logic programming with constraints. The constraints that we consider will not be restricted to statements on real numbers as in CLP(R), see [15]. Instead our constraints will be arbitrary global constraints. The basic idea is that the applicability of a giv ..."
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Cited by 16 (6 self)
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In this note we will investigate a form of logic programming with constraints. The constraints that we consider will not be restricted to statements on real numbers as in CLP(R), see [15]. Instead our constraints will be arbitrary global constraints. The basic idea is that the applicability of a given rule is not predicated on the fact that individual variables satisfy certain constraints, but rather on the fact that the least model of the set rules that are ultimately applicable satisfy the constraint of the rule. Thus the role of clauses will be slightly different than in the usual Logic Programming with constraints. In fact, the paradigm we present is closely related to stable model semantics of general logic programming [13]. We will define the notion of a constraint model of our constraint logic program and show that stable models of logic programs as well as the supported models of logic programs are just special cases of constraint models of constraint logic programs. Our definition of constraint logic programs and constraint models will be quite general. Indeed, in general definition, the constraint of a clause will not be restricted to be of a certain form or even to be expressible in the underlying language of the logic program. This feature is useful for certain applications in hybrid control systems and database applications that we have in mind. However for the most part in this paper, we focus on the properties of constraint programs and constraint models in the simplest case where the constraints are expressible in the
Domain Theory Meets Default Logic
, 1995
"... We present a development of the theory of default information structures, combining ideas from domain theory with ideas from nonmonotonic logic. Conceptually, our treatment is distinguished from standard default logic in that we view default structures as generating models rather than theories. Re ..."
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Cited by 8 (6 self)
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We present a development of the theory of default information structures, combining ideas from domain theory with ideas from nonmonotonic logic. Conceptually, our treatment is distinguished from standard default logic in that we view default structures as generating models rather than theories. Reiter's default rules are viewed as nondeterministic algorithms for generating preferred partial models. Using domaintheoretical notions, we improve the standard definition of extensions in default logic, by introducing the notion of dilation. We prove the existence of such dilations for a new, natural class of default information structures, properly including the socalled seminormal ones. This class, called the class of rational structures, is a robust generalization of the usual kind of default rule system.
Default Timed Concurrent Constraint Programming (Extended Abstract)
, 1995
"... We extend the model of [SJG94b] to express strong timeouts (and preemption): if an event A does not happen through time t, cause event B to happen at time t. Such constructs arise naturally in practice (e.g. in modeling transistors) and are supported in languages such as Esterel (through instanta ..."
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Cited by 8 (1 self)
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We extend the model of [SJG94b] to express strong timeouts (and preemption): if an event A does not happen through time t, cause event B to happen at time t. Such constructs arise naturally in practice (e.g. in modeling transistors) and are supported in languages such as Esterel (through instantaneous watchdogs) and Lustre (through the "current" operator). The fundamental conceptual difficulty posed by these operators is that they are nonmonotonic. We provide a simple compositional semantics to the nonmonotonic version of concurrent constraint programming (CCP) obtained by changing the underlying logic from intuitionistic logic to Reiter 's default logic [Rei80]. This allows us to use the same construction (uniform extension through time) to develop Default Timed CCP (Default tcc) as we had used to develop Timed CCP (tcc) from CCP [SJG94b]. Indeed the smooth embedding of CCP processes into Default cc processes lifts to a smooth embedding of tcc processes into Default t...