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A Modal Analysis of Staged Computation
 JOURNAL OF THE ACM
, 1996
"... We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of functional languages. Our main technical result is a conservative embedding of Nielson & Nielson's twolevel functional language in ..."
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Cited by 185 (22 self)
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We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of functional languages. Our main technical result is a conservative embedding of Nielson & Nielson's twolevel functional language in our language MiniML, which in
The ProofTheory and Semantics of Intuitionistic Modal Logic
, 1994
"... Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpret ..."
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Cited by 102 (0 self)
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Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpreted in an intuitionistic metatheory then the induced modal logics no longer satisfy certain intuitionistically invalid principles. This thesis investigates the intuitionistic modal logics that arise in this way. Natural deduction systems for various intuitionistic modal logics are presented. From one point of view, these systems are selfjustifying in that a possible world interpretation of the modalities can be read off directly from the inference rules. A technical justification is given by the faithfulness of translations into intuitionistic firstorder logic. It is also established that, in many cases, the natural deduction systems induce wellknown intuitionistic modal logics, previously given by Hilbertstyle axiomatizations. The main benefit of the natural deduction systems over axiomatizations is their
Logics for Hybrid Systems
 Proceedings of the IEEE
, 2000
"... This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems ..."
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Cited by 93 (7 self)
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This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems
EXPTIME tableaux for ALC
 ARTIFICIAL INTELLIGENCE
, 2000
"... The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semistructured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIMEcomplete. Second, experiments in automated reaso ..."
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Cited by 51 (3 self)
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The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semistructured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIMEcomplete. Second, experiments in automated reasoning have substantially broadened the meaning of “practical tractability”. Instances of realistic size for PSPACEcomplete problems are now within reach for implemented systems. Still, there is a gap between the reasoning services needed by the expressive logics mentioned above and those provided by the current systems. Indeed, the algorithms based on treeautomata, which are used to prove EXPTIMEcompleteness, require exponential time and space even in simple cases. On the other hand, current algorithms based on tableau methods can take advantage of such cases, but require double exponential time in the worst case. We propose a tableau calculus for the description logic ALC for checking the satisfiability of a concept with respect to a TBox with general axioms, and transform it into the first simple tableaubased decision procedure working in single exponential time. To guarantee the ease of implementation, we also discuss the effects that optimizations (propositional backjumping, simplification, semantic branching, etc.) might have on our complexity result, and introduce a few optimizations ourselves.
SemanticsBased Translation Methods for Modal Logics
, 1991
"... A general framework for translating logical formulae from one logic into another logic is presented. The framework is instantiated with two different approaches to translating modal logic formulae into predicate logic. The first one, the well known ‘relational’ translation makes the modal logic’s po ..."
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Cited by 40 (1 self)
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A general framework for translating logical formulae from one logic into another logic is presented. The framework is instantiated with two different approaches to translating modal logic formulae into predicate logic. The first one, the well known ‘relational’ translation makes the modal logic’s possible worlds structure explicit by introducing a distinguished predicate symbol to represent the accessibility relation. In the second approach, the ‘functional ’ translation method, paths in the possible worlds structure are represented by compositions of functions which map worlds to accessible worlds. On the syntactic level this means that every flexible symbol is parametrized with particular terms denoting whole paths from the initial world to the actual world. The ‘target logic’ for the translation is a firstorder manysorted logic with built in equality. Therefore the ‘source logic’ may also be firstorder manysorted with built in equality. Furthermore flexible function symbols are allowed. The modal operators may be parametrized with arbitrary terms and particular properties of the accessibility relation may be specified within the
Functional Translation and SecondOrder Frame Properties of Modal Logics
, 1995
"... Normal modal logics can be defined axiomatically as Hilbert systems, or semantically in terms of Kripke's possible worlds and accessibility relations. Unfortunately there are Hilbert axioms which do not have corresponding firstorder properties for the accessibility relation. For these logics the ..."
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Cited by 22 (15 self)
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Normal modal logics can be defined axiomatically as Hilbert systems, or semantically in terms of Kripke's possible worlds and accessibility relations. Unfortunately there are Hilbert axioms which do not have corresponding firstorder properties for the accessibility relation. For these logics the standard semanticsbased theorem proving techniques, in particular, the relational translation into firstorder predicate logic, do not work. There is an alternative translation, the socalled functional translation, in which the accessibility relations are replaced by certain terms which intuitively can be seen as functions mapping worlds to accessible worlds. In this paper we show that from a certain point of view this functional language is more expressive than the relational language, and that certain secondorder frame properties can be mapped to firstorder formulae expressed in the functional language. Moreover, we show how these formulae can be computed automatically from the ...
Dynamic topological logic
 Bulletin of Symbolic Logic
, 1997
"... Dynamic Topological Logic provides a context for studying the confluence of the topological semantics for S4, based on topological spaces rather than Kripke frames; topological dynamics; and temporal logic. In the topological semantics for S4, ✷ is interpreted as topological interior: thus S4 can b ..."
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Cited by 21 (3 self)
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Dynamic Topological Logic provides a context for studying the confluence of the topological semantics for S4, based on topological spaces rather than Kripke frames; topological dynamics; and temporal logic. In the topological semantics for S4, ✷ is interpreted as topological interior: thus S4 can be understood as the logic of topological spaces. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Thus, we define a dynamic topological system to be a topological space X together with a continuous function f that can be thought of in temporal terms, moving the points of the topological space from one moment to the next. Dynamic topological logics are the logics of dynamic topological systems, defined for a trimodal language with an S4 topological modality, ✷ (interior), and two temporal modalities, ○ (next) and ∗ (henceforth). One potential area of study is the expressive power of this language: for example, in it one can express the Poincaré Recurrence Theorem. 1
Logicbased specification languages for intelligent software agents
 TPLP
, 2004
"... The research field of AgentOriented Software Engineering (AOSE) aims to find abstractions, languages, methodologies and toolkits for modeling, verifying, validating and prototyping complex applications conceptualized as Multiagent Systems (MASs). A very lively research subfield studies how formal ..."
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Cited by 21 (6 self)
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The research field of AgentOriented Software Engineering (AOSE) aims to find abstractions, languages, methodologies and toolkits for modeling, verifying, validating and prototyping complex applications conceptualized as Multiagent Systems (MASs). A very lively research subfield studies how formal methods can be used for AOSE. This paper presents a detailed survey of six logicbased executable agent specification languages that have been chosen for their potential to be integrated in our ARPEGGIO project, an open framework for specifying and prototyping a MAS. The six languages are ConGolog, AGENT0, the IMPACT agent programming language, Dylog, Concurrent METATEM and Ehhf. For each executable language, the logic foundations are described and an example of use is shown. A comparison of the six languages and a survey of similar approaches complete the paper, together with considerations of the advantages of using logicbased languages in MAS modeling and prototyping.
A Logic Based Framework for Action Theories
 Language, Logic and Computation
, 1996
"... this paper, we present a logic based framework for the representation of actions. Actions can change the meaning of properties of existing constants and their relationships. For instance "take" changes the properties of "on" and "hold": if somebody takes an object lying on a table then he/she will b ..."
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Cited by 16 (4 self)
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this paper, we present a logic based framework for the representation of actions. Actions can change the meaning of properties of existing constants and their relationships. For instance "take" changes the properties of "on" and "hold": if somebody takes an object lying on a table then he/she will be holding this object after performing the action and the object will no longer be on the table. If somebody builds a wall, then the properties of bricks and cement will change. In logic oriented approaches, actions are frequently described by their preconditions and their results. The preconditions are represented by a formula which has to be true before the execution of the action and the results are represented by a formula which will be true after the action has been performed. In addition, the general laws of the world are described by formulas which have always to be true. An action occurs in a state of the world, which is also described by a formula, and yields a new state of the world which is obtained from the old state. Logic based action theories encounter typically the following problems:
Pure extensions, proof rules and hybrid axiomatics
 Preliminary proceedings of Advances in Modal Logic (AiML 2004
, 2004
"... We examine the role played by proof rules in general axiomatisations for hybrid logic. We prove three main results. First, all known axiomatisations for the basic hybrid language ..."
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Cited by 16 (6 self)
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We examine the role played by proof rules in general axiomatisations for hybrid logic. We prove three main results. First, all known axiomatisations for the basic hybrid language