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14
Quantified multimodal logics in simple type theory
, 2009
"... We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple experiments, using existing higherorder theorem provers, to demonstr ..."
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Cited by 14 (12 self)
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We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple experiments, using existing higherorder theorem provers, to demonstrate that the embedding allows automated proofs of statements in these logics, as well as meta properties of them.
Automating access control logics in simple type theory with LEOII
 FB Informatik, U. des Saarlandes
, 2008
"... Abstract Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory and we have demonstrate ..."
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Cited by 11 (9 self)
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Abstract Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory and we have demonstrated that the higherorder theorem prover LEOII can automate reasoning in and about them. In this paper we combine these results and describe a sound (and complete) embedding of different access control logics in simple type theory. Employing this framework we show that the off the shelf theorem prover LEOII can be applied to automate reasoning in and about prominent access control logics. 1
Progress report on LEOII, an automatic theorem prover for higherorder logic
, 2007
"... Abstract. LeoII, a resolution based theorem prover for classical higherorder logic, is currently being developed in a one year research project at the University of Cambridge, UK, with support from Saarland University, Germany. We report on the current stage of development of LeoII. In particular, ..."
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Cited by 10 (6 self)
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Abstract. LeoII, a resolution based theorem prover for classical higherorder logic, is currently being developed in a one year research project at the University of Cambridge, UK, with support from Saarland University, Germany. We report on the current stage of development of LeoII. In particular, we sketch some main aspects of LeoII’s automated proof search procedure, discuss its cooperation with firstorder specialist provers, show that LeoII is also an interactive proof assistant, and explain its shared term data structure and its term indexing mechanism. 1
Multimodal and Intuitionistic Logics in Simple Type Theory
"... We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational inve ..."
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Cited by 9 (9 self)
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We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational investigations of various nonclassical logics. We report some experiments using the higherorder automated theorem prover LEOII.
The LEOII Project
"... LEOII, a resolution based theorem prover for classical higherorder logic, is currently being developed in a one year ..."
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Cited by 6 (0 self)
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LEOII, a resolution based theorem prover for classical higherorder logic, is currently being developed in a one year
Sense and the Computation of Reference
 Linguistics and Philosophy
"... The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends ..."
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Cited by 6 (2 self)
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The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of this relation must be given in the form of a logic program. The resulting system does not only throw light on the properties of sense and their relation to computation, but also shows circular behaviour if some ingredients of the Liar Paradox are added. The connection is natural, as algorithms can be inherently circular and the Liar is explained as expressing one of those. Many ideas in the present paper are closely related to those in Moschovakis (1994), but receive a considerably lighter formalization. 1
Intensional models for the theory of types
 Journal of Symbolic Logic
, 2007
"... In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin’s general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cutfree sequent c ..."
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Cited by 4 (0 self)
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In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin’s general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cutfree sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. 1
MSet Models
"... In [1] Andrews studies elementary type theory, a form of Church’s type theory [12] without extensionality, descriptions, choice, and infinity. Since most of the automated search procedures implemented in Tps [4] do not build in principles of extensionality, descriptions, choice or infinity, they are ..."
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Cited by 2 (1 self)
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In [1] Andrews studies elementary type theory, a form of Church’s type theory [12] without extensionality, descriptions, choice, and infinity. Since most of the automated search procedures implemented in Tps [4] do not build in principles of extensionality, descriptions, choice or infinity, they are essentially
Simple type theory as framework for combining logics
 in Contest paper at the World Congress and School on Universal Logic III (UNILOG’2010
, 2010
"... Abstract. Simple type theory is suited as framework for combining classical and nonclassical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be elegantly embedded in simple type theory. Furthermore ..."
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Cited by 2 (2 self)
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Abstract. Simple type theory is suited as framework for combining classical and nonclassical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be elegantly embedded in simple type theory. Furthermore, simple type theory is sufficiently expressive to model combinations of embedded logics and it has a well understood semantics. Offtheshelf reasoning systems for simple type theory exist that can be uniformly employed for reasoning within and about combinations of logics. 1
Verifying the Modal Logic Cube is an Easy Task (for HigherOrder Automated Reasoners)
"... Abstract. Prominent logics, including quantified multimodal logics, can be elegantly embedded in simple type theory (classical higherorder logic). Furthermore, offtheshelf reasoning systems for simple type type theory exist that can be uniformly employed for reasoning within and about embedded lo ..."
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Cited by 2 (2 self)
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Abstract. Prominent logics, including quantified multimodal logics, can be elegantly embedded in simple type theory (classical higherorder logic). Furthermore, offtheshelf reasoning systems for simple type type theory exist that can be uniformly employed for reasoning within and about embedded logics. In this paper we focus on reasoning about modal logics and exploit our framework for the automated verification of inclusion and equivalence relations between them. Related work has applied firstorder automated theorem provers for the task. Our solution achieves significant improvements, most notably, with respect to elegance and simplicity of the problem encodings as well as with respect to automation performance. 1