Proceedings of the 13 ESSLLI Student Session - Multiple Choices ...

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Proceedings of the 13 th ESSLLI Student Session complementing the UML’s visual nature (Kent, 1997). The constraint diagram in figure 1 shows a constraint in a library management system. Amongst other things it states that people can only borrow books that are in the collections of libraries they have joined. Figure 1: A constraint diagram and an Euler diagram. There are many reasons that we might want to use diagrams to represent information, including the potential of diagrams for well matchedness and free rides. A diagram is well matched to its subject if it presents the key features of that subject effectively and in a way that seems intuitively clear to the viewer (Gurr and Tourlas, 2000). A well matched diagram can make certain reasoning tasks appear to be easier when compared with a symbolic representation of the same information. Free rides occur when a diagram provides some information ‘naturally’ or ‘for free’ which would need to be explicitly stated in, or derived from, a symbolic representation (Shimojima, 2004). For example, in the Euler diagram in figure 1, the fact that the contour Spaniels is placed within GunDogs asserts directly that Spaniels ⊆ GunDogs but also allows the viewer to infer Spaniels ⊆ Dogs and Spaniels ∩ Cats = ∅. Details of well matchedness and free rides in constraint diagrams can be found in (Stapleton and Delaney, 2008). In some circumstances the expressive power of diagrams can produce ambiguity, or lead the viewer to make false inferences. However, many diagrammatic notations now have formal, unambiguous semantics, of which Euler and constraint diagrams are prominent examples. Our ultimate goal is to create a Domain Specific Embedded Language (DSEL) for several systems of diagrammatic reasoning, with two main aims: to explore the benefits and boundaries of the emerging style of programming that mixes formal methods with programming, and to support the work which aims to establish visual logics as a valuable tool in formal methods. The DSEL will be written in Haskell and will consist of statically verified code which will allow the user to manipulate and reason with a variety of visual logics such as Euler diagrams, spider diagrams and constraint diagrams (see Section 2). The DSEL, therefore, shares one of the primary aims of visual logics — to make formal reasoning more accessible and widely used. Reasoning about design and implementation have traditionally taken place in separate phases of the software process, with the onus on the programmer to bridge the gap between the two. One of the benefits of combining both activities in one phase is that constraints modelled by a programmer using the DSEL will form software components in their own right, resulting in diagrams with the same type as functions in 48
Proceedings of the 13 th ESSLLI Student Session the modelled system. This suggests that such constraints could eventually form part of working software, perhaps as part of a “trusted kernel” used by other components, following the approach of (Kiselyov and Shan, 2007). The form and function of the DSEL will therefore be closely linked — a formally specified language to assist formal reasoning. Advances in Programming Language Theory are typically explored in research languages before percolating into more widely used languages. This is especially true of modern functional languages and, in particular, Haskell. The Haskell type system with the extensions provided by the GHC compiler make it possible to explore what Sheard called (when speaking of the closely related language Ωmega) “a new point in the design space of formal reasoning systems — part programming language, part logical framework” (Sheard, 2004) and to do so directly within the environment of a practical language with efficient implementations. The language features that enable this can be used to emulate the behaviour of fully dependently typed languages such as Epigram (Altenkirch, Mcbride and Mckinna, 2005), resulting in what have been called “pseudo-dependently typed” systems, described in Section 4. The syntactic clarity, referential transparency and similarity to mathematical notation of functional languages are also of benefit to us. These features help us in our goal to minimise syntactic differences between the DSEL and the diagrammatic logics we implement, making it easier to demonstrate a clear mapping between the two. The point of this mapping is to demonstrate “literal preservation of syntactic relations under denotation”, as Hammer states the conditions for resemblance between a sign and that which it signifies (Hammer, 1995). In Section 2 we describe reasoning with Euler diagrams. Section 3 gives an overview of type theoretic features making their way into programming languages while Section 4 looks ahead to the form our DSEL will take, using Euler diagrams as a case study. In Section 5 we consider the goals of the research, evaluate the strategies used to reach them and identify some of the challenges ahead. 2 Reasoning with Euler diagrams Although diagrams have often been used to aid understanding in mathematical proofs, they have until fairly recently been treated as informal and secondary to formalized symbolic content. In the 1990s the work of Shin began to put diagrams on a different standing by proving soundness and completeness results for the Venn-II reasoning system, an extension and formalisation of earlier work by Venn and Peirce (Shin, 1994). Stapleton provides a summary of the history of diagrammatic reasoning since then, which is now a rapidly evolving and active research area (Stapleton, 2007). What makes such logics interesting, given the existence of mature symbolic reasoning techniques, is the combination of formal reasoning with the compact and intuitive nature of diagrams referred to previously. We expect that this, and the efforts to create supporting tools, will make formal reasoning more accessible to non-logicians. An Euler diagram is a collection of closed curves called contours which represent sets, within an enclosing rectangle. Figure 2 shows an example with three contours, labelled A, B and C. Containment, intersection and disjointness are represented by the placement of contours, so the same diagram asserts C ⊆ A and B ∩ C = ∅. A zone is a set of points in the diagram that can be described as being inside certain contours and outside all others. The diagram in figure 2 has five zones; one inside A but outside B and C, one 49
Page 1 and 2: Proceedings of the 13 th ESSLLI Stu
Page 3 and 4: Contents Preface . . . . . . . . .
Page 5 and 6: Preface Proceedings of the 13 th ES
Page 9 and 10: mechanism of the encoded function.
Page 13 and 14: The table below presents experiment
Page 17 and 18: SIMULATING SPOKEN DIALOGUE WITH A F
Page 19 and 20: 21 Speech Generation Speech generat
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Page 33 and 34: 3 Comparison With a Partition Seman
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Page 37 and 38: BARE PREDICATION AND KINDS ∗ Bert
Page 39 and 40: The reason why the b-variants are o
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Page 43 and 44: 43 Non-bare predication and non-uni
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Page 47: DIAGRAMMATIC REASONING WITH ENHANCE
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Page 53 and 54: type theory of Euler diagrams based
Page 55 and 56: software (Stapleton and Delaney, 20
Page 57 and 58: FICTIONAL CONTINGENCIES Gemma Celes
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Page 75 and 76: TOWARDS A NEW CHARACTERISATION OF C
Page 77 and 78: The following paper continues this
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Page 89 and 90: Results The percentages of correct
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Page 95 and 96: A SALIENCE-DRIVEN APPROACH TO SPEEC
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2. the linguistic salience or “re
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Proceedings of the 13 th ESSLLI Stu
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where the expectations provided by
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A LOGIC WITH A CONDITIONAL PROBABIL
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• v : F orC × W −→ {0, 1} is
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Lemma 4 M ∗ is a measurable model
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is a tautology. Now we can equivale
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A PROOF-THEORETIC APPROACH TO FRENC
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References Abeillé, A., Godard, D.
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INFINITE GAMES FROM AN INTUITIONIST
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6 Further problems Proceedings of t
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pointers to the text, containing th
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example in a comparatively short te
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Such an example is: Constant modifi
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WORD SPACE MODELS OF SEMANTIC SIMIL
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tween semantic similarity and seman
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wu & palmer 0.0 0.2 0.4 0.6 0.8 1.0
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frequency F−score 0 100 200 300 4
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EXAMINING THE NOTICING FUNCTION OF
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effects of input flood and individu
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CDIPROVER3: A TOOL FOR PROVING DERI
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Example 8. Consider the TRS given i
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THE RANK(S) OF A TOTALLY LEXICALIST
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EXPRESSING CONJUNCTIVE AND AGGREGAT
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(Rule) (Semantic Action) Qwh → In
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(⇐) We will prove, by induction o
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1 Introduction INTERROGATION IN DYN
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to hold for questions to be felicit
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5 Further research One goal for a s
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THE SEMANTIC CHANGE OF THE FRENCH -
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6 Conclusion In this paper, I inves
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ADVERSARY IMPLICATURES ∗ Grégoir
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2.2.1 The derivation of Q-Implicatu
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of the first, the relation of Contr
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List of authors Martin Avanzini Mar
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