## The Heterogeneous Tool Set (2007)

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Venue: | of Lecture Notes in Computer Science |

Citations: | 32 - 21 self |

### BibTeX

@INPROCEEDINGS{Mossakowski07theheterogeneous,

author = {Till Mossakowski and Christian Maeder and Klaus Lüttich and Stefan Wölfl},

title = {The Heterogeneous Tool Set},

booktitle = {of Lecture Notes in Computer Science},

year = {2007},

pages = {519--522},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

Abstract. Heterogeneous specification becomes more and more important because complex systems are often specified using multiple viewpoints, involving multiple formalisms. Moreover, a formal software development process may lead to a change of formalism during the development. However, current research in integrated formal methods only deals with ad-hoc integrations of different formalisms. The heterogeneous tool set (Hets) is a parsing, static analysis and proof management tool combining various such tools for individual specification languages, thus providing a tool for heterogeneous multi-logic specification. Hets is based on a graph of logics and languages (formalized as so-called institutions), their tools, and their translations. This provides a clean semantics of heterogeneous specification, as well as a corresponding proof calculus. For proof management, the calculus of development graphs (known from other large-scale proof management systems) has been adapted to heterogeneous specification. Development graphs provide an overview of the (heterogeneous) specification module hierarchy and the current proof state, and thus may be used for monitoring the overall correctness of a heterogeneous development. 1

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Citation Context ... CASL-DL is an extension of a restriction of CASL, realizing a strongly typed variant of OWL DL in CASL syntax. SPASS [46] is an automatic theorem prover for first-order logic with equality. Isabelle =-=[39]-=- is an interactive theorem prover for higher-order logic. SPASS and Isabelle are the only logics coming with a prover. Proof support for the other logics can be obtained by using logic translations to... |

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Citation Context ...he past 25 years, a large number of calculi for efficient reasoning about spatial and temporal entities have been developed. A prominent example of that kind are the various region connection calculi =-=[38]-=-. In the region connection calculus RCC8, which also has become a GIS standard, it is possible to express relations between regions (= regular closed sets) in a metric space. The set of RCC8 base rela... |

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Citation Context ...al (homogeneous) logics and logic translations. To be definite, the terms ’logic’ and ’logic translation’ need to be formalized in a precise mathematical sense. We here use the notions of institution =-=[17]-=- and entailment system [28], and of comorphism [43] between these. Logical theories are usually formulated over some (user-defined) vocabulary, hence it is assumed that an institution provides a notio... |

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Citation Context ...Haskell-program. Another challenge is the integration of proof planners into HETS. Finally, there is work in progress about the meta-level specification of institutions and their comorphisms in Twelf =-=[37]-=-, which shall lead to correctness proofs for the comorphisms integrated into HETS. Acknowledgement This work has been supported by the project MULTIPLE of the Deutsche Forschungsgemeinschaft under gra... |

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Citation Context ...f CASL, realizing a strongly typed variant of OWL DL in CASL syntax. SoftFOL [21] offers three automated theorem proving (ATP) systems for first-order logic with equality: (1) SPASS [45]; (2) Vampire =-=[39]-=-; and (3) MathServ Broker 5 [47]. These together comprise some of the most advanced theorem provers for first-order logic. Isabelle [34] is an interactive theorem prover for higher-order logic, and (j... |

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Citation Context ... logic translations. To be definite, the terms ’logic’ and ’logic translation’ need to be formalized in a precise mathematical sense. We here use the notions of institution [17] and entailment system =-=[28]-=-, and of comorphism [43] between these. Logical theories are usually formulated over some (user-defined) vocabulary, hence it is assumed that an institution provides a notion of signature. Especially ... |

130 | OMDoc – An open markup format for mathematical documents [Version 1.2
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Citation Context ...s, while the different formal semantics that have been developed for UML would be represented as logic translations.) Likewise, languages for mathematical knowledge management like OpenMath and OMDoc =-=[18]-=- are deliberately only semi-formal. Service integration approaches like MathWeb [48] are either informal, or based on a fixed formalism. Moreover, there are many bi- or trilateral combinations of diff... |

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Citation Context ...nstants, (x,y), with x < y. For the instants-from-intervals approach we start with a first-order specification of intervals. For example, we could use a version of Allen and Hayes’ first order theory =-=[2, 19]-=-, which characterizes intervals in terms of a single binary relation M (read as: “meets” or “immediately precedes”). The CASL specification of this theory, ALLENHAYES, contains structural axioms such ... |

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Citation Context ...eton type the only purpose of which is to determine all other type components of the given logic. 4sIn Haskell jargon, the interface is called a multiparameter type class with functional dependencies =-=[41]-=-. The Haskell interface for logic translations is realised similarly. 4 Logics Available in Hets The degree of support of different languages by HETS is shown in Fig. 3. In this section we give a shor... |

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Citation Context ...class citizens. This can be compared with the treatment of theory morphisms as first-class citizens, which is a distinctive feature of formalisms like OMDoc [18] and tools like Specware [17] and IMPS =-=[12, 11]-=-. A clear referencing of symbols to their theories can distinguish, for example, the naturals with zero from the naturals without zero, even if they are denoted with the same symbol Nat. Theory morphi... |

80 | Proof General: A generic tool for proof development
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Citation Context ...) comorphism. For the automatic theorem prover SPASS [46] a new window is opened which controls the prover calls (Fig. 8). Isabelle [39], a semi automatic theorem prover, is started with ProofGeneral =-=[4]-=- in a separate Emacs. The ’Close’ button allows for integrating the status of the goals’ list back into the development graph. If all goals have been proved, this theory’s node turns from red into gre... |

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Citation Context ...terogeneous parser transforms a string conforming to the syntax in Fig. 4 to an abstract syntax tree and is additionally parameterized over an arbitrary logic graph, using theParsec combinator parser =-=[24]-=-. Logic and translation names are looked up in the logic graph — this is necessary to be able to choose the correct parser for basic specifications. Indeed, the 7sparser has a state that carries the c... |

47 |
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Citation Context ...nto a proved supported logic. It is assumed that all comorphisms are model-expansive, which means that borrowing of entailment systems along the composite comorphism ρ = (Φ,α,β) is sound and complete =-=[13, 34]-=-: Theorem 3. (Σ,Γ ) |= I Σ ϕ iff (Φ(Σ),α(Γ )) |= J αΣ (ϕ). That is, if entailment ⊢ captures sematic consequence |=, we can re-use the prover along the (composite) comorphism. For the automatic theore... |

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Citation Context ...://www.w3c.org). It is used for knowledge representation and the Semantic Web [8]. CASL-DL is an extension of a restriction of CASL, realizing a strongly typed variant of OWL DL in CASL syntax. SPASS =-=[46]-=- is an automatic theorem prover for first-order logic with equality. Isabelle [39] is an interactive theorem prover for higher-order logic. SPASS and Isabelle are the only logics coming with a prover.... |

40 | The PROSPER Toolkit
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Citation Context ...lisms, consider e.g. the integrated formal methods conference series [3, 18, 12, 11]. Integrations of multiple decision procedures and model checkers into theorem provers, like in the PROSPER toolkit =-=[15]-=-, provide a more systematic approach. Still, these approaches are uni-lateral in the sense that there is one logic (and one theorem prover, like the HOL prover) which serves as the central integration... |

37 | Towards an evolutionary formal software-development using CASL
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- 2000
(Show Context)
Citation Context ... in HETS is the formalism of development graphs. Development graphs have been used for large industrial-scale applications with hundreds of specifications [20]. They also support management of change =-=[5]-=-. The graph structure provides a direct visualization of the structure of specifications, and it also allows for managing large specifications with hundreds of sub-specifications. Tools such as MAYA [... |

33 | Logical representations for automated reasoning about spatial relationships
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Citation Context ...ation in metric spaces. This verification goal can be split into two subgoals: 1. Verification that closed discs in a metric (cf. node RCC FO in Fig. 7) satisfy some of Bennett’s connectedness axioms =-=[4]-=- (cf. nodeMetricSpace in Fig. 7). RCC FO consists of very few (actually, 4) theorems, so-called bridge lemmas. SinceMetricSpace is a higher-order theory, they need to be translated to higherorder logi... |

32 |
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Citation Context ... institutions — all that is needed is captured by the satisfaction condition.s122 Till Mossakowski, Christian Maeder, Klaus Lüttich Different logical formalisms are related by institution comorphisms =-=[13]-=-, which are again governed by the satisfaction condition, this time expressing that truth is invariant also under change of notation across different logical formalisms: M ′ |= J Φ(Σ) αΣ(ϕ) ⇔ βΣ(M ′ )... |

31 |
Heterogeneous Specification and the Heterogeneous Tool Set. Habilitation thesis
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Citation Context ...slates (along the intra- and inter-logic translations) the theory, while simultaneously adding nodes and links to the development graph. The static analysis follows a so-called verification semantics =-=[34]-=-, which satisfies the following theorem: Theorem 1. The development graph given by the verification semantics has the same signature and model class (in the Grothendieck institution) as the heterogene... |

30 |
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Citation Context ...rsa, points from intervals we use first an auxiliary specification CONSTRUCTPOINTSFO (for reasons that will be discussed in sec. 9), which extends ALLENHAYES by two 4-ary relations Equi and Less (cf. =-=[22, 23]-=-): 2 logic CASL spec CONSTRUCTPOINTSFO[ALLENHAYES] = %def preds Equi , Less : Elem × Elem × Elem × Elem ∀x,y,z,u : Elem • x y Equi z u ⇔ x M y ∧ z M u ∧ x M u • x y Less z u ⇔ x M y ∧ z M u ∧ (∃v : El... |

29 | Automation for interactive proof: First prototype
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(Show Context)
Citation Context ...just provides a combination of some first-order provers and Isabelle, and the reader may wonder what the advantage of HETS is when compared to an ad-hoc combination of Isabelle and such provers, like =-=[22]-=-. But already now, HETS provides proof support for modal logic (via the translation to CASL, and then further to either SPASS or Isabelle), as well as for COCASL. Hence, it is quite easy to provide pr... |

26 | CSP-Casl -- a new integration of process algebra and algebraic specification
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(Show Context)
Citation Context ... [40] is a modern, pure and strongly typed functional programming language. It simultaneously is the implementation language of HETS, such that in the future, HETS might be applied to itself. CspCASL =-=[42]-=- is a combination of CASL with the process algebra CSP. OWL DL is the Web Ontology Language (OWL) recommended by the World Wide Web Consortium (W3C,http://www.w3c.org). It is used for knowledge repres... |

25 | Development graphs – proof management for structured specifications
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(Show Context)
Citation Context ...node, while a local theorem only postulates that the local axioms of the source node hold in the target node. Theorem links are initially displayed in red. 1 The proof calculus for development graphs =-=[35, 37, 34]-=- is given by rules that allow for proving global theorem links by decomposing them into simpler (local and global) ones. Theorem links that have been 1 The red colour is only available when displaying... |

24 | HasCasl: Towards integrated specification and development of Haskell programs
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- 2002
(Show Context)
Citation Context ...with multi-modalities and term modalities. It allows the specification of modal systems with Kripke’s possible worlds semantics. It is also possible to express certain forms of dynamic logic. HasCASL =-=[45]-=- is a higher order extension of CASL allowing polymorphic datatypes and functions. It is closely related to the programming language Haskell and allows program constructs being embedded in the specifi... |

24 |
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Citation Context ...Σ ϕ iff (Φ(Σ),α(Γ)) |= J αΣ(ϕ). That is, if the entailment ⊢ generated by the prover captures semantic consequence |=, we can re-use the prover along the (composite) comorphism. In the terminology of =-=[1]-=-, (Σ,Γ) |= I Σ ϕ in institution I captures the what to prove, while its translation to institution J captures the how to prove. Additionally, this interface offers to select in detail the axioms and p... |

22 |
System description: The mathweb software bus for distributed mathematical reasoning
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(Show Context)
Citation Context ...presented as logic translations.) Likewise, languages for mathematical knowledge management like OpenMath and OMDoc [18] are deliberately only semi-formal. Service integration approaches like MathWeb =-=[48]-=- are either informal, or based on a fixed formalism. Moreover, there are many bi- or trilateral combinations of different formalisms; consider e.g. the integrated formal methods conference series [41]... |

21 | P.: Short Time Periods
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Citation Context ...nstants, (x,y), with x < y. For the instants-from-intervals approach we start with a first-order specification of intervals. For example, we could use a version of Allen and Hayes’ first order theory =-=[2, 19]-=-, which characterizes intervals in terms of a single binary relation M (read as: “meets” or “immediately precedes”). The CASL specification of this theory, ALLENHAYES, contains structural axioms such ... |

21 | Composing hidden information modules over inclusive institutions. In From Object Orientation to Formal Methods: Dedicated to the memory of Ole-Johan Dahl, volume 2635
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Citation Context ...be definite, the terms ’logic’ and ’logic translation’ need to be formalized in a precise mathematical sense. We here use the notions of institution [17] and entailment system [28], and of comorphism =-=[43]-=- between these. Logical theories are usually formulated over some (user-defined) vocabulary, hence it is assumed that an institution provides a notion of signature. Especially for modular 2sFig. 1. Ar... |

20 |
Grothendieck institutions. Applied Categorical Structures, 10(4):383–402, 2002. Preliminary version appeared as
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(Show Context)
Citation Context ...is completely different from CASL’s. Moreover, support of further structuring languages is planned. The semantics of HETCASL specifications is given in terms of the so-called Grothendieck institution =-=[16, 31]-=-. This institution is basically a flattening, or disjoint union, of the logic graph. A signature in the Grothendieck institution consists of a pair (L,Σ) where L is a logic and Σ is a signature in the... |

20 | Comorphism-based grothendieck logics
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(Show Context)
Citation Context ...is completely different from CASL’s. Moreover, support of further structuring languages is planned. The semantics of HETCASL specifications is given in terms of the so-called Grothendieck institution =-=[16, 31]-=-. This institution is basically a flattening, or disjoint union, of the logic graph. A signature in the Grothendieck institution consists of a pair (L,Σ) where L is a logic and Σ is a signature in the... |

19 | B.: Functional design and implementation of graphical user interfaces for theorem provers
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(Show Context)
Citation Context ...%implies • AGF ∃x : Elem. 〈write.x〉true end Fig. 9. A specification of fair buffers in CASL, CSP-CASL and MODALCASL. There is related work about generic parsers, user interfaces, theorem provers etc. =-=[39, 26, 25]-=-. However, these approaches are mostly limited to genericity, and do not support real heterogeneity, that is the simultaneous use of different formalisms. Technically, genericity often is implemented ... |

16 |
The Development Graph Manager MAYA (system description
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(Show Context)
Citation Context ...]. The graph structure provides a direct visualization of the structure of specifications, and it also allows for managing large specifications with hundreds of sub-specifications. Tools such as MAYA =-=[6]-=- provide a management of proofs, based on the formalism of development graphs. The goal of HETS is to make MAYA heterogeneous. A development graph (see Fig. 6 for an example) consists of a set of node... |

15 |
The Completeness of a Natural System for Reasoning with Time Intervals
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- 1987
(Show Context)
Citation Context ...rsa, points from intervals we use first an auxiliary specification CONSTRUCTPOINTSFO (for reasons that will be discussed in sec. 9), which extends ALLENHAYES by two 4-ary relations Equi and Less (cf. =-=[22, 23]-=-): 2 logic CASL spec CONSTRUCTPOINTSFO[ALLENHAYES] = %def preds Equi , Less : Elem × Elem × Elem × Elem ∀x,y,z,u : Elem • x y Equi z u ⇔ x M y ∧ z M u ∧ x M u • x y Less z u ⇔ x M y ∧ z M u ∧ (∃v : El... |

15 | An infrastructure for intertheory reasoning
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(Show Context)
Citation Context ...class citizens. This can be compared with the treatment of theory morphisms as first-class citizens, which is a distinctive feature of formalisms like OMDoc [18] and tools like Specware [17] and IMPS =-=[12, 11]-=-. A clear referencing of symbols to their theories can distinguish, for example, the naturals with zero from the naturals without zero, even if they are denoted with the same symbol Nat. Theory morphi... |

14 |
Algebraic-coalgebraic specification
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- 2006
(Show Context)
Citation Context ...olymorphic variables) in the types for signatures, morphisms, abstract syntax etc. This eases integration of CASL extensions and keeps the effort of integrating CASL extensions quite moderate. CoCASL =-=[38]-=- is a coalgebraic extension of CASL, suited for the specification of process types and reactive system. The central proof method is coinduction. ModalCASL is an extension of CASL with multi-modalities... |

12 | OMDoc: An Infrastructure for OpenMath Content Dictionary Information
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(Show Context)
Citation Context ...ferent formal semantics that have been developed for UML in the meantime would be represented as logic translations.) Likewise, languages for mathematical knowledge management like OpenMath and OMDoc =-=[21]-=- are deliberately only semi-formal. Service integration approaches like MathWeb [47], Modelware [1] or JETI [27] are either informal, or based on a fixed formalism. Moreover, there are many bi- or tri... |

12 | Formal Interoperability
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(Show Context)
Citation Context ... complexity of large software systems, it is a fact of life that no single perspective, no single formalization of level of abstraction suffices to represent a system and reason about its behaviour.” =-=[29]-=- “As can be seen, a plethora of formalisms for the verification of programs, and, in particular, for the verification of concurrent programs has been proposed. . . . there are good reasons to consider... |

11 | TAS and IsaWin: Tools for transformational program development and theorem proving
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(Show Context)
Citation Context ...%implies • AGF ∃x : Elem. 〈write.x〉true end Fig. 9. A specification of fair buffers in CASL, CSP-CASL and MODALCASL. There is related work about generic parsers, user interfaces, theorem provers etc. =-=[39, 26, 25]-=-. However, these approaches are mostly limited to genericity, and do not support real heterogeneity, that is the simultaneous use of different formalisms. Technically, genericity often is implemented ... |

10 | Foundations of heterogeneous specification
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(Show Context)
Citation Context ...ent graph for fair buffer specification in CASL, CSP-CASL and MODALCASL Future work will integrate more logics and interface more existing theorem proving tools with specific institutions in HETS. In =-=[32]-=-, we have presented a heterogeneous specification with more diverse formalisms, namely CSP-CASL and a temporal logic (as part of MODALCASL). An example is shown in Fig. 9. CSP-CASL is used to describe... |

10 |
Răzvan Diaconescu, and Andrzej Tarlecki, What is a logic translation
- Mossakowski
(Show Context)
Citation Context ...s to sentences and models to models, such that satisfaction is preserved (where models are mapped contravariantly, i.e. against the direction of the comorphism). We refer the reader to the literature =-=[17, 28, 36]-=- for formal details of institutions and comorphisms. Subsequently, we use the terms “institution” and “logic” interchangeably, as well as the terms “institution comorphism” and “logic translation”. 3 ... |

10 |
and Andrzej Tarlecki. Essential Concepts of Algebraic Specification and Program Development
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(Show Context)
Citation Context ...et is shown in Fig. 2 on page 123. In the sequel, we will explain the details of this figure. 2 Heterogeneous Specifications: the Model-Theoretic View We take a model-theoretic view on specifications =-=[42]-=-. This means that the notion of logical theory (i.e. collection of axioms) is considered to be only an auxiliary concept, and the meaning of a formal specification (of a program module) is given by – ... |

10 |
The MathServe System for Semantic Web Reasoning Services
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- 2006
(Show Context)
Citation Context ...ed variant of OWL DL in CASL syntax. SoftFOL [21] offers three automated theorem proving (ATP) systems for first-order logic with equality: (1) SPASS [45]; (2) Vampire [39]; and (3) MathServ Broker 5 =-=[47]-=-. These together comprise some of the most advanced theorem provers for first-order logic. Isabelle [34] is an interactive theorem prover for higher-order logic, and (jointly with others) marks the fr... |

9 | Reasoning Support for CASL with Automated Theorem Proving Systems
- Lüttich, Mossakowski
- 2007
(Show Context)
Citation Context ...w3c.org). It is used for knowledge representation and the Semantic Web [5]. CASL-DL [20] is an extension of a restriction of CASL, realizing a strongly typed variant of OWL DL in CASL syntax. SoftFOL =-=[21]-=- offers three automated theorem proving (ATP) systems for first-order logic with equality: (1) SPASS [45]; (2) Vampire [39]; and (3) MathServ Broker 5 [47]. These together comprise some of the most ad... |

8 |
HetCasl - heterogeneous specification. Language summary
- Mossakowski
- 2004
(Show Context)
Citation Context ...is the implementation of the logic. The arrows denote logic translations (comorphisms). Proof support can be obtained by following a path to a prover-supported logic. Heterogeneous CASL (HETCASL; see =-=[33]-=-) includes the structuring constructs of CASL, such as union and translation. A key feature of CASL is that syntax and semantics of these constructs are formulated over an arbitrary institution (i.e. ... |

8 | zChaff: Modifications and extensions
- Herbstritt
(Show Context)
Citation Context ... is realised similarly. 4 Logics Available in Hets In this section we give a short overview of the logics available in HETS. Propositional is classical propositional logic, with the zChaff SAT solver =-=[15]-=- connected to it. CASL extends many sorted first-order logic with partial functions and subsorting. It also provides induction sentences, expressing the (free) generation of datatypes. For more detail... |

7 | B.: jeti: A tool for remote tool integration
- Margaria, Nagel, et al.
(Show Context)
Citation Context ...ons.) Likewise, languages for mathematical knowledge management like OpenMath and OMDoc [21] are deliberately only semi-formal. Service integration approaches like MathWeb [47], Modelware [1] or JETI =-=[27]-=- are either informal, or based on a fixed formalism. Moreover, there are many bi- or trilateral combinations of different formalisms, consider e.g. the integrated formal methods conference series [3, ... |

7 | Institutional 2-cells and grothendieck institutions. In Essays Dedicated to - Mossakowski - 2006 |

6 |
Verification of Reactive Systems
- Schneider
- 2004
(Show Context)
Citation Context ... in particular, for the verification of concurrent programs has been proposed. . . . there are good reasons to consider all the mentioned formalisms, and to use whichever one best suits the problem.” =-=[44]-=- (italics in the original) In the area of formal specification and logics used in computer science, numerous logics are in use: – logics for specification of datatypes, – process calculi and logics fo... |

5 |
Ontologies for the semantic web
- Mossakowski, Lttich, et al.
- 2004
(Show Context)
Citation Context ... to itself. OWL DL is the Web Ontology Language (OWL) recommended by the World Wide Web Consortium (W3C, http://www.w3c.org). It is used for knowledge representation and the Semantic Web [5]. CASL-DL =-=[20]-=- is an extension of a restriction of CASL, realizing a strongly typed variant of OWL DL in CASL syntax. SoftFOL [21] offers three automated theorem proving (ATP) systems for first-order logic with equ... |

5 | Qualitative constraint calculi: Heterogeneous verification of composition tables
- Wölfl, Mossakowski, et al.
- 2007
(Show Context)
Citation Context ...cess is error-prone, and we already have found errors in published composition tables. Hence, formal verification of composition tables (w.r.t. their semantic interpretation) is an important task. In =-=[46]-=-, we present a heterogeneous verification of the RCC8 composition table w.r.t. the interpretation in metric spaces. This verification goal can be split into two subgoals: 1. Verification that closed d... |