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The Foundation of a Generic Theorem Prover
 Journal of Automated Reasoning
, 1989
"... Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized. Isabell ..."
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Cited by 471 (49 self)
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Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized. Isabelle is now based on higherorder logic  a precise and wellunderstood foundation. Examples illustrate use of this metalogic to formalize logics and proofs. Axioms for firstorder logic are shown sound and complete. Backwards proof is formalized by metareasoning about objectlevel entailment. Higherorder logic has several practical advantages over other metalogics. Many proof techniques are known, such as Huet's higherorder unification procedure. Key words: higherorder logic, higherorder unification, Isabelle, LCF, logical frameworks, metareasoning, natural deduction Contents 1 History and overview 2 2 The metalogic M 4 2.1 Syntax of the metalogic ......................... 4 2.2 ...
Invertibility in Sequent Calculi
 The Archive of Formal Proofs. http://afp.sourceforge.net/entries/ SequentInvertibility.shtml
, 2009
"... Abstract. The invertibility of the rules of a sequent calculus is important for guiding proof search and can be used in some formalised proofs of Cut admissibility. We present sufficient conditions for when a rule is invertible with respect to a calculus. We illustrate the conditions with examples. ..."
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Abstract. The invertibility of the rules of a sequent calculus is important for guiding proof search and can be used in some formalised proofs of Cut admissibility. We present sufficient conditions for when a rule is invertible with respect to a calculus. We illustrate the conditions with examples
Countermodels from Sequent Calculi in MultiModal Logics
, 2012
"... A novel countermodelproducing decision procedure that applies to several multimodal logics, both intuitionistic and classical, is presented. Based on backwards search in labeled sequent calculi, the procedure employs a novel termination condition and countermodel construction. Using the procedure, ..."
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A novel countermodelproducing decision procedure that applies to several multimodal logics, both intuitionistic and classical, is presented. Based on backwards search in labeled sequent calculi, the procedure employs a novel termination condition and countermodel construction. Using the procedure
Equality Reasoning in SequentBased Calculi
 Handbook of Automated Reasoning, volume I, chapter 10
, 1996
"... Contents i Introduction ........................................ 613 1.1 Some useful notation ................................ 614 1.2 Equality. The first axiomatization ......................... 615 1.3 Paramodulation and its refinements ........................ 616 1.4 Equality in sequent systems ..."
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Cited by 23 (7 self)
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Contents i Introduction ........................................ 613 1.1 Some useful notation ................................ 614 1.2 Equality. The first axiomatization ......................... 615 1.3 Paramodulation and its refinements ........................ 616 1.4 Equality in sequent
Modal Sequent Calculi Labelled with Truth Values: Completeness, Duality and Analyticity
 LOGIC JOURNAL OF THE IGPL
, 2003
"... Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessi ..."
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Cited by 8 (5 self)
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Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties
Logic in Computer Science: Modelling and Reasoning about Systems
, 1999
"... ion. ACM Transactions on Programming Languages and Systems, 16(5):15121542, September 1994. Bibliography 401 [Che80] B. F. Chellas. Modal Logic  an Introduction. Cambridge University Press, 1980. [Dam96] D. R. Dams. Abstract Interpretation and Partition Refinement for Model Checking. PhD thesi ..."
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Cited by 345 (11 self)
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ion. ACM Transactions on Programming Languages and Systems, 16(5):15121542, September 1994. Bibliography 401 [Che80] B. F. Chellas. Modal Logic  an Introduction. Cambridge University Press, 1980. [Dam96] D. R. Dams. Abstract Interpretation and Partition Refinement for Model Checking. Ph
Modal Languages And Bounded Fragments Of Predicate Logic
, 1996
"... Model Theory. These are nonempty families I of partial isomorphisms between models M and N , closed under taking restrictions to smaller domains, and satisfying the usual BackandForth properties for extension with objects on either side  restricted to apply only to partial isomorphisms of size ..."
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Cited by 271 (12 self)
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Model Theory. These are nonempty families I of partial isomorphisms between models M and N , closed under taking restrictions to smaller domains, and satisfying the usual BackandForth properties for extension with objects on either side  restricted to apply only to partial isomorphisms of size
G.L.: Nested Sequent Calculi for Conditional Logics
 Logics in Artificial Intelligence  13th European Conference, JELIA 2012. Lecture Notes in Artificial Intelligence (LNAI
, 2012
"... Abstract. Nested sequent calculi are a useful generalization of ordinary sequent calculi, where sequents are allowed to occur within sequents. Nested sequent calculi have been profitably employed in the area of (multi)modal logic to obtain analytic and modular proof systems for these logics. In th ..."
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Cited by 3 (2 self)
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Abstract. Nested sequent calculi are a useful generalization of ordinary sequent calculi, where sequents are allowed to occur within sequents. Nested sequent calculi have been profitably employed in the area of (multi)modal logic to obtain analytic and modular proof systems for these logics
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