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Reasoning on UML Class Diagrams
 ARTIFICIAL INTELLIGENCE
, 2003
"... UML is the defacto standard formalism for software design and analysis. To support the design of largescale industrial applications, sophisticated CASE tools are available on the market, that provide a userfriendly environment for editing, storing, and accessing multiple UML diagrams. It would ..."
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Cited by 96 (23 self)
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UML is the defacto standard formalism for software design and analysis. To support the design of largescale industrial applications, sophisticated CASE tools are available on the market, that provide a userfriendly environment for editing, storing, and accessing multiple UML diagrams. It would be highly desirable to equip such CASE tools with automated reasoning capabilities in order to detect relevant formal properties of UML diagrams, such as inconsistencies or redundancies. With regard to this issue, we consider UML class diagrams, which are one of the most important components of UML, and we address the problem of reasoning on such diagrams. We resort to several results developed in the eld of Description Logics (DLs), a family of logics that admit decidable reasoning procedures.
Tableau calculi for answer set programming
 PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING (ICLP’06
, 2006
"... We introduce a formal proof system based on tableau methods for analyzing computations made in Answer Set Programming (ASP). Our approach furnishes declarative and finegrained instruments for characterizing operations as well as strategies of ASPsolvers. First, the granulation is detailed enough ..."
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Cited by 18 (7 self)
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We introduce a formal proof system based on tableau methods for analyzing computations made in Answer Set Programming (ASP). Our approach furnishes declarative and finegrained instruments for characterizing operations as well as strategies of ASPsolvers. First, the granulation is detailed enough to capture the variety of propagation and choice operations of algorithms used for ASP; this also includes SATbased approaches. Second, it is general enough to encompass the various strategies pursued by existing ASPsolvers. This provides us with a uniform framework for identifying and comparing fundamental properties of algorithms. Third, the approach allows us to investigate the proof complexity of algorithms for ASP, depending on choice operations. We show that exponentially different bestcase computations can be obtained for different ASPsolvers. Finally, our approach is flexible enough to integrate new inference patterns, so to study their relation to existing ones. As a result, we obtain a novel approach to unfounded set handling based on loops, being applicable to nonSATbased solvers. Furthermore, we identify backward propagation operations for unfounded sets.
Knowledge Representation and Classical Logic
"... Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspe ..."
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Cited by 10 (4 self)
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Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspective of knowledge representation, their formal languages were not sufficiently expressive. On the other hand, most logicians were not concerned about the possibility of automated reasoning; from the perspective of knowledge representation, they were often too generous in the choice of syntactic constructs. In spite of these differences, classical mathematical logic has exerted significant influence on knowledge representation research, and it is appropriate to begin this handbook with a discussion of the relationship between these fields. The language of classical logic that is most widely used in the theory of knowledge representation is the language of firstorder (predicate) formulas. These are the formulas that John McCarthy proposed to use for representing declarative knowledge in his advice taker paper [176], and Alan Robinson proposed to prove automatically using resolution [236]. Propositional logic is, of course, the most important subset of firstorder logic; recent
Proving programs incorrect using a sequent calculus for Java Dynamic Logic
 Proceedings, International Conference on Tests and Proofs (TAP
, 2007
"... Abstract. Program verification is concerned with proving that a program is correct and adheres to a given specification. Testing a program, in contrast, means to search for a witness that the program is incorrect. In the present paper, we use a program logic for Java to prove the incorrectness of pr ..."
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Cited by 8 (0 self)
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Abstract. Program verification is concerned with proving that a program is correct and adheres to a given specification. Testing a program, in contrast, means to search for a witness that the program is incorrect. In the present paper, we use a program logic for Java to prove the incorrectness of programs. We show that this approach, carried out in a sequent calculus for dynamic logic, creates a connection between calculi and proof procedures for program verification and test data generation procedures. Starting with a program logic enables to find more general and more complicated counterexamples for the correctness of programs.
Tableau Reasoning and Programming with Dynamic First Order Logic
, 2001
"... Dynamic First Order Logic (DFOL) results from interpreting quantification over a variable v as change of valuation over the v position, conjunction as sequential composition, disjunction as nondeterministic choice, and negation as (negated) test for continuation. We present a tableau style calculus ..."
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Cited by 5 (4 self)
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Dynamic First Order Logic (DFOL) results from interpreting quantification over a variable v as change of valuation over the v position, conjunction as sequential composition, disjunction as nondeterministic choice, and negation as (negated) test for continuation. We present a tableau style calculus for DFOL with explicit (simultaneous) binding, prove its soundness and completeness, and point out its relevance for programming with DFOL, for automated program analysis including loop invariant detection, and for semantics of natural language. Next, we extend this to an infinitary calculus for DFOL with iteration and connect up with other work in dynamic logic.
A Model Generation Style Completeness Proof for Constraint Tableaux with Superposition
, 2002
"... We present a calculus that integrates equality handling by superposition into a free variable tableau calculus. We prove completeness of this calculus by an adaptation of the model generation [1, 15] technique commonly used for completeness proofs of resolution calculi. ..."
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Cited by 4 (2 self)
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We present a calculus that integrates equality handling by superposition into a free variable tableau calculus. We prove completeness of this calculus by an adaptation of the model generation [1, 15] technique commonly used for completeness proofs of resolution calculi.
Autonomous Learning of Commonsense Simulations
"... Parameterdriven simulations are an effective and efficient method for reasoning about a wide range of commonsense scenarios that can complement the use of logical formalizations. The advantage of simulation is its simplified knowledge elicitation process: rather than building complex logical formul ..."
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Cited by 4 (2 self)
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Parameterdriven simulations are an effective and efficient method for reasoning about a wide range of commonsense scenarios that can complement the use of logical formalizations. The advantage of simulation is its simplified knowledge elicitation process: rather than building complex logical formulae, simulations are constructed by simply selecting numerical values and graphical structures. In this paper, we propose the application of machine learning techniques to allow an embodied autonomous agent to automatically construct appropriate simulations from its realworld experience. The automation of learning can dramatically reduce the cost of knowledge elicitation, and therefore result in models of commonsense with breadth and depth not possible with traditional engineering of logical formalizations.
Fast decision procedure for propositional dummett logic based on a multiple premise tableau calculus
, 2008
"... We present a procedure to decide propositional Dummett logic. This procedure relies on a tableau calculus with a multiple premise rule and optimizations. The resulting implementation outperforms the state of the art graphbased procedure. 1 ..."
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Cited by 3 (2 self)
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We present a procedure to decide propositional Dummett logic. This procedure relies on a tableau calculus with a multiple premise rule and optimizations. The resulting implementation outperforms the state of the art graphbased procedure. 1
Tableaux, Path Dissolution, and Decomposable Negation Normal Form for Knowledge Compilation
"... Decomposable negation normal form (DNNF) was developed primarily for knowledge compilation. Formulas in DNNF are linkless, in negation normal form (NNF), and have the property that atoms are not shared across conjunctions. Full dissolvents are linkless NNF formulas that do not in general have the la ..."
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Cited by 2 (0 self)
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Decomposable negation normal form (DNNF) was developed primarily for knowledge compilation. Formulas in DNNF are linkless, in negation normal form (NNF), and have the property that atoms are not shared across conjunctions. Full dissolvents are linkless NNF formulas that do not in general have the latter property. However, many of the applications of DNNF can be obtained with full dissolvents. Two additional methods — regular tableaux and semantic factoring — are shown to produce equivalent DNNF. A class of formulas is presented on which earlier DNNF conversion techniques are necessarily exponential; path dissolution and semantic factoring handle these formulas in linear time.
Labelled Clauses
"... Abstract. We add labels to firstorder clauses to simultaneously apply superpositions to several proof obligations inside one clause set. From a theoretical perspective, the approach unifies a variety of deduction modes. These include different strategies such as set of support, as well as explicit ..."
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Cited by 2 (1 self)
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Abstract. We add labels to firstorder clauses to simultaneously apply superpositions to several proof obligations inside one clause set. From a theoretical perspective, the approach unifies a variety of deduction modes. These include different strategies such as set of support, as well as explicit case analysis, e.g., splitting. From a practical perspective, labelled clauses offer advantages in the case of related proof obligations resulting from multiple conjectures over the same axiom set or from a single conjecture that is a large conjunction. Here we can share clauses (e.g., the axioms and clauses deduced from them, share Skolem symbols), share deduced clause variants, and transfer lemmas between the different obligations. Motivated by software verification, we have created a prototype implementation of labelled clauses that supports multiple conjectures, and we provide convincing experiments for the benefits. 1