Semantic and inferencing abilities in children with communication disorders

Background: Semantic and inferencing abilities have not been fully examined in children with communication difficulties. Aims: To investigate the inferential and semantic abilities of children with communication difficulties using newly designed tasks. Methods & Procedures: Children with different types of communication disorder were compared with each other and with three groups of typically developing children: those of the same chronological age and two groups of younger children. In total, 25 children aged 11 years with specific language impairment and 22 children, also 11 years of age, with primary pragmatic difficulties were recruited. Typically developing groups aged 11 (n = 35; age‐match), and those aged 9 (n = 40) and 7 (n = 37; language similar) also participated as comparisons. Outcomes & Results: For Semantic Choices, children with specific language impairment performed significantly more poorly than 9‐ and 11‐year‐olds, whilst the pragmatic difficulties group scored significantly lower than all the typically developing groups. Borderline differences between specific language impairment and pragmatic difficulties groups were found. For inferencing, children with communication impairments performed significantly below the 11‐year‐old peers, but not poorer than 9‐ and 7‐year‐olds, suggesting that this skill is in line with language ability. Six children in the pragmatic difficulties group who met diagnosis for autism performed more poorly than the other two clinical groups on both tasks, but not statistically significantly so. Conclusions: Both tasks were more difficult for those with communication impairments compared with peers. Semantic but not inferencing abilities showed a non‐significant trend for differences between the two clinical groups and children with pragmatic difficulties performed more poorly than all typically developing groups. The tasks may relate to each other in varying ways according to type of communication difficulty

A Terminating Evaluation-Driven Variant of G3i

We present Gbu, a terminating variant of the sequent calculus G3i for intuitionistic propositional logic. Gbu modifies G3i by annotating the sequents so to distinguish rule applications into two phases: an unblocked phase where any rule can be backward applied, and a blocked phase where only right rules can be used. Derivations of Gbu have a trivial translation into G3i. Rules for right implication exploit an evaluation relation, defined on sequents; this is the key tool to avoid the generation of branches of infinite length in proof-search. To prove the completeness of Gbu, we introduce a refutation calculus Rbu for unprovability dual to Gbu. We provide a proof-search procedure that, given a sequent as input, returns either a Rbu-derivation or a Gbu-derivation of it

Sequent Calculus in the Topos of Trees

Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of trees. We show that the semantics of the propositional fragment of this logic can be given by linear converse-well-founded intuitionistic Kripke frames, so this logic is a marriage of the intuitionistic modal logic KM and the intermediate logic LC. We therefore call this logic $\mathrm{KM}_{\mathrm{lin}}$. We give a sound and cut-free complete sequent calculus for $\mathrm{KM}_{\mathrm{lin}}$ via a strategy that decomposes implication into its static and irreflexive components. Our calculus provides deterministic and terminating backward proof-search, yields decidability of the logic and the coNP-completeness of its validity problem. Our calculus and decision procedure can be restricted to drop linearity and hence capture KM.Comment: Extended version, with full proof details, of a paper accepted to FoSSaCS 2015 (this version edited to fix some minor typos

Music Teacher Education at a Liberal Arts College

In 2012, a committee at a small Midwestern liberal arts college, Lake Forest College, embarked on a journey to create a music education teacher licensure major. Drawing from narrative inquiry, this article reports how the dean of faculty, education department chair, music department chair, and assistant professor of music/music education coordinator collaborated on a curricular creation. Findings from this process included (a) the created music education major, (b) each participant’s rationale for wanting the new music education major, (c) valued components of the music education major, and (d) unique elements of a music education major at a liberal arts college. Implications from this experience could be valuable for music education programs at small liberal arts colleges, those involved in university/school partnerships such as professional development schools, and those looking to advocate for their music education programs across campus

BCDL : Basic Constructive Description Logic

In this paper we present BCDL, a description logic based on information terms semantics, which allows a constructive interpretation of ALC formulas. In the paper we describe the information terms semantics, we define a natural deduction calculus for BCDL and we show it is sound and complete. As a first application of proof-theoretical properties of the calculus, we show how it fulfills the proofs-as-programs paradigm. Finally, we discuss the role of generators, the main element distinguishing our formalisation from the usual ones

Simplification rules for intuitionistic propositional tableaux

The implementation of a logic requires, besides the definition of a calculus and a decision procedure, the development of techniques to reduce the search space. In this article we introduce some simplification rules for Intuitionistic propositional logic that try to replace a formula with an equi-satisfiable \u201csimpler\u201d one with the aim to reduce the search space. Our results are proved via semantical techniques based on Kripke models. We also provide an empirical evaluation of their impact on implementations

A secondary semantics for second order intuitionistic propositional logic

In this paper we propose a Kripke-style semantics for second order intuitionistic propositional logic and we provide a semantical proof of the disjunction and the explicit definability property. Moreover, we provide a tableau calculus which is sound and complete with respect to such a semantics

JTabWb : a Java framework for implementing terminating sequent and tableau calculi

JTabWb is a Java framework for developing provers based on terminating sequent or tableau calculi. It provides a generic engine which performs proof-search driven by a user-de ned speci cation. The user is required to de ne the components of a prover by implementing suitable Java interfaces. The implemented provers can be used as standalone applications or embedded in other Java applications. The framework also supports proof-trace generation, LATEX rendering of proofs and counter-model generation

On the complexity of the disjunction property in intuitionistic and modal logics

In this paper we study the complexity of disjunction property for Intuitionistic Logic, the modal logics S3, S4.1, Grzegorczyk Logic, Godel-Lob Logic and the intuitionistic counterpart of the modal logic K. For S4 we even prove the feasible interpolation theorem and we provide a lower bound for the length of proofs. The techniques we use do not require to prove structural properties of the calculi in hand, such as the Cut-elimination Theorem or the Normalization Theorem. This is a key-point of our approach, since it allows us to treat logics for which only Hilbert-style characterizations are known