Related papers: Equality, Quasi-Implicit Products, and Large Elimi…

Many economic theory models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness…

We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…

Predicate-argument structure analysis is a central component in meaning representations of text. The fact that some arguments are not explicitly mentioned in a sentence gives rise to ambiguity in language understanding, and renders it…

Coping with ambiguous questions has been a perennial problem in real-world dialogue systems. Although clarification by asking questions is a common form of human interaction, it is hard to define appropriate questions to elicit more…

We prove "untyping" theorems: in some typed theories (semirings, Kleene algebras, residuated lattices, involutive residuated lattices), typed equations can be derived from the underlying untyped equations. As a consequence, the…

Simple type theory is formulated for use with the generic theorem prover Isabelle. This requires explicit type inference rules. There are function, product, and subset types, which may be empty. Descriptions (the eta-operator) introduce the…

The depth-bounded fragment of the pi-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system,…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…

Type-and-effect systems help the programmer to organize data and computational effects in a program. While for traditional type systems expressive variants with sophisticated inference algorithms have been developed and widely used in…

We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…

We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…

Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…

Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…

We present a version of arithmetic in all finite types which allows for a definition of equality at higher types for which all congruence are derivable, for which the soundness of the Dialectica interpretation is provable inside the system…

We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.

The word problem for categories with free products and coproducts (sums), SP-categories, is directly related to the problem of determining the equivalence of certain processes. Indeed, the maps in these categories may be directly…

We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…

We study the Hardy type inequalities in the framework of equalities. We present equalities which immediately imply Hardy type inequalities by dropping the remainder term. Simultaneously we give a characterization of the class of functions…

Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…

We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…