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54
A Logic of Argumentation for Reasoning under Uncertainty.
 Computational Intelligence
, 1995
"... We present the syntax and proof theory of a logic of argumentation, LA. We also outline the development of a category theoretic semantics for LA. LA is the core of a proof theoretic model for reasoning under uncertainty. In this logic, propositions are labelled with a representation of the arguments ..."
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Cited by 145 (8 self)
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We present the syntax and proof theory of a logic of argumentation, LA. We also outline the development of a category theoretic semantics for LA. LA is the core of a proof theoretic model for reasoning under uncertainty. In this logic, propositions are labelled with a representation of the arguments which support their validity. Arguments may then be aggregated to collect more information about the potential validity of the propositions of interest. We make the notion of aggregation primitive to the logic, and then define strength mappings from sets of arguments to one of a number of possible dictionaries. This provides a uniform framework which incorporates a number of numerical and symbolic techniques for assigning subjective confidences to propositions on the basis of their supporting arguments. These aggregation techniques are also described, with examples. Key words: Uncertain reasoning, epistemic probability, argumentation, nonclassical logics, nonmonotonic reasoning 1. Introd...
Representation and Inference for Natural language  A First Course in . . .
, 1999
"... 3.672> X with the complex term 1 + 1, not with 2, which, for people unused to Prolog's little ways, tends to come as a bit of a surprise. If we want to carry out the actual arithmetic involved, we have to explicitly force evaluation by making use of the very special inbuilt `operator' ..."
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Cited by 102 (11 self)
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3.672> X with the complex term 1 + 1, not with 2, which, for people unused to Prolog's little ways, tends to come as a bit of a surprise. If we want to carry out the actual arithmetic involved, we have to explicitly force evaluation by making use of the very special inbuilt `operator' is/2. This calls an inbuilt mechanism which carries out the arithmetic evaluation of its second argument, and then unication plays no role here!). On the other hand, \== checks whether its argument are not identical. Arithmetic Prolog contains some builtin operators for handling integer arithmetic. These include *, / +,  (for multiplication, division, addition, and subtraction, respectively) and >, < for comparing numbers. These symbols, however, are just ordinary Prolog operators. That is, they are just a user friendly notation for writing
Proof Normalization Modulo
, 1998
"... We consider a class of logical formalisms, in which firstorder logic is extended by identifying propositions modulo a given congruence. We particularly focus on the case where this congruence is induced by a confluent and terminating rewrite system over the propositions. This extension enhances the ..."
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Cited by 70 (20 self)
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We consider a class of logical formalisms, in which firstorder logic is extended by identifying propositions modulo a given congruence. We particularly focus on the case where this congruence is induced by a confluent and terminating rewrite system over the propositions. This extension enhances the power of firstorder logic and various formalisms, including higherorder logic, can be described in this framework. We conjecture that proof normalization and logical consistency always hold over this class of formalisms, provided some minimal conditions over the rewrite system are fulfilled. We prove this conjecture for some subcases, including higherorder logic. At last, we extend these results to classical sequent calculus.
Monotonic and Residuated Logic Programs
, 2001
"... In this paper we define the rather general framework of Monotonic Logic Programs, where the main results of (definite) logic programming are validly extrapolated. Whenever defining new logic programming extensions, we can thus turn our attention to the stipulation and study of its intuitive algebrai ..."
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Cited by 58 (10 self)
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In this paper we define the rather general framework of Monotonic Logic Programs, where the main results of (definite) logic programming are validly extrapolated. Whenever defining new logic programming extensions, we can thus turn our attention to the stipulation and study of its intuitive algebraic properties within the very general setting. Then, the existence of a minimum model and of a monotonic immediate consequences operator is guaranteed, and they are related as in classical logic programming. Afterwards we study the more restricted class of residuated logic programs which is able to capture several quite distinct logic programming semantics. Namely: Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic Logic Programming. We provide the embedding of possibilistic logic programming.
A Brief Guide to Linear Logic
, 1993
"... An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation. ..."
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Cited by 56 (10 self)
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An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation.
Antitonic Logic Programs
, 2001
"... In a previous work we have de ned Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truthvalues with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, ..."
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Cited by 46 (11 self)
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In a previous work we have de ned Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truthvalues with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs and Fuzzy Logic Programming [3, 4]. However, none of these semantics define a form of nonmonotonic negation, which is fundamental for several knowledge representation applications. In the spirit of our previous work, we generalise our framework of Monotonic Logic Programs to allow for rules with arbitrary antitonic bodies over general complete lattices, of which normal programs are a special case. We then show that all the standard logic programming theoretical results carry over to Antitonic Logic Programs, defining Stable Model and Wellfounded Model alike semantics.
From the Specification of Multiagent Systems by Statecharts to their Formal Analysis by Model Checking
, 2001
"... A formalism for the specification of multiagent systems should be expressive and illustrative enough to model not only the behavior of one single agent, but also the collaboration among several agents and the influences caused by external events from the environment. For this, state machines [25] ..."
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Cited by 44 (5 self)
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A formalism for the specification of multiagent systems should be expressive and illustrative enough to model not only the behavior of one single agent, but also the collaboration among several agents and the influences caused by external events from the environment. For this, state machines [25] seem to provide an adequate means. Furthermore, it should be easily possible to obtain an implementation for each agent automatically from this specification. Last but not least, it is desirable to be able to check whether the multiagent system satisfies some interesting properties. Therefore, the formalism should also allow for the verification or formal analysis of multiagent systems, e.g. by model checking [6]. In this paper, a framework is introduced, which allows us to express declarative aspects of multiagent systems by means of (classical) propositional logic and procedural aspects of these systems by means of state machines (statecharts). Nowadays statecharts are a well accepted means to specify dynamic behavior of software systems. They are a part of the Unified Modeling Language (UML). We describe in a rigorously formal manner, how the specification of spatial knowledge and robot interaction and its verification by model checking can be done, integrating different methods from the field of artificial intelligence such as qualitative (spatial) reasoning and the situation calculus. As example application domain, we will consider robotic soccer, see also [24, 31], which present predecessor work towards a formal logicbased approach for agents engineering.
A Compiler for Natural Semantics
 6TH INTERNATIONAL CONFERENCE ON COMPILER CONSTRUCTION, CC'96, LINKÖPING
, 1996
"... Natural semantics is a formalism used for specifying both semantics and implementations of programming languages. Until recently, no practical implementation of the formalism existed. We have defined the Relational MetaLanguage, RML, as an executable specification language for natural semantics. Af ..."
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Cited by 40 (2 self)
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Natural semantics is a formalism used for specifying both semantics and implementations of programming languages. Until recently, no practical implementation of the formalism existed. We have defined the Relational MetaLanguage, RML, as an executable specification language for natural semantics. After a brief outline of the language, we describe the compilation strategy used by our rml2c compiler: transformations are applied to minimize nondeterminism, and a continuationpassing style form is produced and simplified. Finally the CPS is emitted as lowlevel C code, using an efficient technique for implementing tailcalls. We also present performance measurements that support our choice of compilation strategy.
Monodic temporal resolution
 ACM Transactions on Computational Logic
, 2003
"... Until recently, FirstOrder Temporal Logic (FOTL) has been only partially understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However, a breakthrough by Hodkinson et al., identifying a f ..."
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Cited by 31 (15 self)
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Until recently, FirstOrder Temporal Logic (FOTL) has been only partially understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However, a breakthrough by Hodkinson et al., identifying a finitely axiomatisable fragment, termed the monodic fragment, has led to improved understanding of FOTL. Yet, in order to utilise these theoretical advances, it is important to have appropriate proof techniques for this monodic fragment. In this paper, we modify and extend the clausal temporal resolution technique, originally developed for propositional temporal logics, to enable its use in such monodic fragments. We develop a specific normal form for monodic formulae in FOTL, and provide a complete resolution calculus for formulae in this form. Not only is this clausal resolution technique useful as a practical proof technique for certain monodic classes, but the use of this approach provides us with increased understanding of the monodic fragment. In particular, we here show how several features of monodic FOTL can be established as corollaries of the completeness result for the clausal temporal resolution method. These include definitions of new decidable monodic classes, simplification of existing monodic classes by reductions, and completeness of clausal temporal resolution in the case of
Foundations of canonical update support for closed database views
 ICDT’90, Third International Conference on Database Theory
, 1990
"... A closed view of a database schema is one which is totally encapsulated. Insofar as the user is concerned, the view is the database schema. The rest of the database system is not visible through the view, and is is not required for complete use of the view. Similarly, the updates which may be effect ..."
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Cited by 30 (9 self)
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A closed view of a database schema is one which is totally encapsulated. Insofar as the user is concerned, the view is the database schema. The rest of the database system is not visible through the view, and is is not required for complete use of the view. Similarly, the updates which may be effected through the view have their scope limited entirely to that view. In this paper, we lay the mathematical foundations for the systematic support of such views. The proper context is shown to be that of update translation under constant meet complement, a refinement of the constant complement strategy of Bancilhon and Spyratos. The central complexity result for relational schemata is that checking the legality of updates is “infinitely ” simpler than blindly checking that the new state is legal for the view schema, and in the particular case that the base schema is constrained by functional dependencies, may always be performed in constant time, even if the view schema is not finitely axiomatizable. We further establish that, under very natural assumptions, update strategies for closed views are unique.