Cubical type theory provides a constructive justification to certain aspects of homotopy type theory such as Voevodsky’s univalence axiom. This makes many extensionality principles, like function and propositional extensionality, directly provable in the theory. This paper describes a constructive semantics, expressed in a presheaf topos with suitable structure inspired by cubical sets, of some...

We define a higher-order extension of Datalog based on the Horn fragment of higher-order logic introduced in [Wad91]. Programs of Higher-Order Datalog can be understood declaratively as formulas in extensional higher-order logic, in which (for example) a unary predicate of unary predicates is a set of sets of data objects. The language retains all the basic principles of first-order logic progr...

We suggest a three-level integrated approach to design, specification and verification of distributed system. The approach is based on a newly designed specification language Basic-REAL (bREAL) and comprises (I) translation of a high-level design of distributed systems to executional specifications of bREAL, (II) presentation of high-level properties of distributed systems as logical specificat...

Optimality Theory catches on in linguistics, rst in phonology, then in syntax , and recently also at the semantics / pragmatics interface. In this paper we point at some parallels between principles employed in optimality the-oretic interpretation, and notions from the well-established eld of Game Theory. Optimality theoretic interpretation can be deened as what we call an \interpretation game"...

We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying numbers of inputs, quotiented to alpha-equivalence and sorted according to a binding signature. The theory includes a rich collection of properties of the sta...

The theory of nominal sets is a rich mathematical framework for studying syntax and variable binding. Within it, we can describe several binding disciplines and derive convenient reasoning principles that are compatible with u�-equivalence. In this article, we introduce the notion of binding operator, a novel construction on nominal sets that unifies and generalizes the many forms of binding pr...

Sequences of speech sounds play a central role in human cognitive life, and the principles that govern such sequences are crucial in determining the syntax and semantics of natural languages. Infants are capable of extracting both simple transitional probabilities and simple algebraic rules from sequences of speech, as demonstrated by studies using ABB grammars (la ta ta, gai mu mu, etc.). Here...

Universal Grammar and statistical generalization from linguistic data have almost always been invoked as mutually exclusive means of explaining child language acquisition. This papers show that such segregation is both conceptually unnecessary and empirically flawed. We demonstrate the utility of general learning mechanisms in the acquisition of the core grammatical system through frequency eff...

SCEL is a new language specifically designed to model autonomic components and their interaction. It brings together various programming abstractions that permit to directly represent knowledge, behaviors and aggregations according to specific policies. It also supports naturally programming self-awareness, context-awareness, and adaptation. In this paper, we first present design principles, sy...