This work extends the existing MACE-style finite model finding approach to multi-sorted first-order logic. This existing approach iteratively assumes increasing domain sizes and encodes the related ground problem as a SAT problem. When moving to the multi-sorted setting each sort may have a different domain size, leading to an explosion in the search space. This paper focusses on methods to tam...

LIFE uses matching on order-sorted feature structures for passing arguments to functions. As opposed to uni cation which amounts to normalizing a conjunction of constraints, solving a matching problem consists of deciding whether a constraint (guard) or its negation are entailed by the context. We give a complete and consistent set of rules for entailment and disentailment of order-sorted featu...

We usually use natural language vocabulary for sort names in order-sorted logics, and some sort names may contradict other sort names in the sort-hierarchy. These implicit negations, called lexical negations in linguistics, are not explicitly prefixed by the negation connective. In this paper, we propose the notions of structured sorts, sort relations, and the contradiction in the sort-hierarch...

A tournament Tn is an orientation of a complete graph on n vertices. A king in a tournament is a vertex from which every other vertex is reachable by a path of length at most 2. A sorted sequence of kings in a tournament Tn is an ordered list of its vertices u1, u2, . . . , un such that ui dominates ui+1 (ui → ui+1) and ui is a king in the subtournament induced by {uj : i ≤ j ≤ n} for each i = ...

This paper studies sorted generalization-the generalization, with respect to an arbitrary taxonomic theory, of atomic formulas containing sorted variables. It develops an algorithm for the task, discusses the algorithm and task complexity, and presents semantic properties of sorted generalization. Based on its semantic properties, we show how sorted generalization is applicable to such problems...

We consider the problem of approximating a convex gure in the plane by a pair r R of homothetic that is similar and parallel rectangles with r C R We show the existence of such a pair where the sides of the outer rectangle are at most twice as long as the sides of the inner rectangle thereby solving a problem posed by P olya and Szeg o If the n vertices of a convex polygon C are given as a sort...

syntax Set ADJ 1975 S-sorted abstract syntax Set Robinson 1994 Abstract syntax with binding SetF Fiore,Plotkin,Turi 1999 Recursive path ordring LO R. Hasegawa 2002 S-sorted 2nd-order abs. syn. (SetF↓S)S Fiore 2003 2nd-order rewriting systems PreF Hamana 2005 Explicit substitutions [Set,Set]f Ghani,Uustalu,Hamana 2006 Cyclic sharing structures (SetT ∗ )T Hamana 2009

The introduction of sorts in rst-order automatic theorem proving has been accompanied by a considerable gain in computational eeciency via reduced search spaces. This suggests that sort information can be employed in higher-order theorem proving with similar results. This paper develops an order-sorted higher-order calculus suitable for automatic theorem proving applications | by extending the ...

Assume we are interested in solving a computational task, e.g., sorting n numbers, and we only have access to an unreliable primitive operation, for example, comparison between two numbers. Suppose that each primitive operation fails with probability at most p and that repeating it is not helpful, as it will result in the same outcome. Can we still approximately solve our task with probability ...