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Michael Thielscher - One of the best experts on this subject based on the ideXlab platform.

  • A Theory of First-Order Counterfactual Reasoning
    2007
    Co-Authors: Michael Thielscher
    Abstract:

    A new theory of evaluating counterfactual statements is presented based on the established Predicate Calculus formalism of the Fluent Calculus for reasoning about actions. The assertion of a counterfactual antecedent is axiomatized as the performance of a special action

  • The Concurrent, Continuous Fluent Calculus
    Studia Logica, 2001
    Co-Authors: Michael Thielscher
    Abstract:

    The Fluent Calculus belongs to the established Predicate Calculus formalisms for reasoning about actions. Its underlying concept of state update axioms provides a solution to the basic representational and inferential Frame Problems in pure first-order logic. Extending a recent research result, we present a Fluent Calculus to reason about domains involving continuous change and where actions occur concurrently.

  • a new equational foundation for the fluent Calculus
    Lecture Notes in Computer Science, 2000
    Co-Authors: Hans-peter Storr, Michael Thielscher
    Abstract:

    A new equational foundation is presented for the Fluent Calculus, an established Predicate Calculus formalism for reasoning about actions. We discuss limitations of the existing axiomatizations of both equality of states and what it means for a fluent to hold in a state. Our new and conceptually even simpler theory is shown to overcome the restrictions of the existing approach. We prove that the correctness of the Fluent Calculus as a solution to the Frame Problem still holds under the new foundation. Furthermore, we extend our theory by an induction axiom needed for reasoning about integer-valued resources.

  • A New Equational Foundation for the Fluent Calculus
    Kluwer Academic, 2000
    Co-Authors: Hans-peter Storr, Michael Thielscher
    Abstract:

    . A new equational foundation is presented for the Fluent Calculus, an established Predicate Calculus formalism for reasoning about actions. We discuss limitations of the existing axiomatizations of both equality of states and what it means for a fluent to hold in a state. Our new and conceptually even simpler theory is shown to overcome the restrictions of the existing approach. We prove that the correctness of the Fluent Calculus as a solution to the Frame Problem still holds under the new foundation. Furthermore, we extend our theory by an induction axiom needed for reasoning about integer-valued resources. Stream: Knowledge Representation and Non-monotonic Reasoning 1 Introduction Research in Cognitive Robotics aims at explaining and modeling high-level intelligent agents acting in a complex dynamic world. Among the established Predicate Calculus formalisms for reasoning about actions, the Fluent Calculus stands out in offering a solution not only to the representational..

  • continuous processes in the fluent Calculus
    1999
    Co-Authors: Michael Thielscher
    Abstract:

    Among the known Predicate Calculus formalisms for axiomatizing commonsense reasoning about actions, the Fluent Calculus stands out in offering a solution not only to the representational but also the inferential aspect of the fundamental Frame Problem. In this paper we extend this formalism to modeling hybrid systems, which involve both discrete and continuous change. We borrow basic notions from an existing extension of the Situation Calculus to this end, but depart from it in a crucial aspect: Exogenous events are uncoupled from the action sequence performed by the agent. In this way we solve the problem of non-existence of simple plans caused by incomplete knowledge of the ongoing processes, and we enable solutions to Zeno’s paradox.

Simonov Anton - One of the best experts on this subject based on the ideXlab platform.

Wil Dekkers - One of the best experts on this subject based on the ideXlab platform.

  • Completeness of two systems of illative combinatory logic for first-order propositional and Predicate Calculus
    Archive for Mathematical Logic, 1998
    Co-Authors: Wil Dekkers, Martin W. Bunder, Henk Barendregt
    Abstract:

    Illative combinatory logic consists of the theory of combinators or lambda Calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers 4 systems of illative combinatory logic that are sound for first-order propositional and Predicate Calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators, or in a more direct way, in which derivations are not translated. Both translations are closely related in a canonical way. In a preceding paper, Barendregt, Bunder and Dekkers, 1993, we proved completeness of the two direct translations. In the present paper we prove completeness of the two indirect translations by showing that the corresponding illative systems are conservative over the two systems for the direct translations. In another version, DBB (1997), we shall give a more direct completeness proof. These papers fulfill the program of Church and Curry to base logic on a consistent system of \(\lambda\)-terms or combinators. Hitherto this program had failed because systems of ICL were either too weak (to provide a sound interpretation) or too strong (sometimes even inconsistent).

  • Systems of illative combinatory logic complete for first-order propositional and Predicate Calculus
    Journal of Symbolic Logic, 1993
    Co-Authors: Henk Barendregt, Martin W. Bunder, Wil Dekkers
    Abstract:

    Illative combinatory logic consists of the theory of combinators or lambda Calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers systems of illative combinatory logic that are sound for first-order propositional and Predicate Calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators or, in a more direct way, in which derivations are not translated. Both translations are closely related in a canonical way. The two direct translations turn out to be complete. The paper fulfills the program of Church [1932], [1933] and Curry [1930] to base logic on a consistent system of A-terms or combinators. Hitherto this program had failed because systems of ICL were either too weak (to provide a sound interpretation) or too strong (sometimes even inconsistent). ?

Henk Barendregt - One of the best experts on this subject based on the ideXlab platform.

  • Completeness of two systems of illative combinatory logic for first-order propositional and Predicate Calculus
    Archive for Mathematical Logic, 1998
    Co-Authors: Wil Dekkers, Martin W. Bunder, Henk Barendregt
    Abstract:

    Illative combinatory logic consists of the theory of combinators or lambda Calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers 4 systems of illative combinatory logic that are sound for first-order propositional and Predicate Calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators, or in a more direct way, in which derivations are not translated. Both translations are closely related in a canonical way. In a preceding paper, Barendregt, Bunder and Dekkers, 1993, we proved completeness of the two direct translations. In the present paper we prove completeness of the two indirect translations by showing that the corresponding illative systems are conservative over the two systems for the direct translations. In another version, DBB (1997), we shall give a more direct completeness proof. These papers fulfill the program of Church and Curry to base logic on a consistent system of \(\lambda\)-terms or combinators. Hitherto this program had failed because systems of ICL were either too weak (to provide a sound interpretation) or too strong (sometimes even inconsistent).

  • Systems of illative combinatory logic complete for first-order propositional and Predicate Calculus
    Journal of Symbolic Logic, 1993
    Co-Authors: Henk Barendregt, Martin W. Bunder, Wil Dekkers
    Abstract:

    Illative combinatory logic consists of the theory of combinators or lambda Calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers systems of illative combinatory logic that are sound for first-order propositional and Predicate Calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators or, in a more direct way, in which derivations are not translated. Both translations are closely related in a canonical way. The two direct translations turn out to be complete. The paper fulfills the program of Church [1932], [1933] and Curry [1930] to base logic on a consistent system of A-terms or combinators. Hitherto this program had failed because systems of ICL were either too weak (to provide a sound interpretation) or too strong (sometimes even inconsistent). ?

Daowu Pei - One of the best experts on this subject based on the ideXlab platform.

  • a fuzzy logic for an ordinal sum t norm
    Fuzzy Sets and Systems, 2005
    Co-Authors: Sanmin Wang, Baoshu Wang, Daowu Pei
    Abstract:

    Among the class of residuated fuzzy logics, a few of them have been shown to have standard completeness both for propositional and Predicate Calculus, like Godel, NM and monoidal t-norm-based logic systems. In this paper, a new residuated logic NMG, which aims at capturing the tautologies of a class of ordinal sum t-norms and their residua, is introduced and its standard completeness both for propositional Calculus and for Predicate Calculus are proved.