A Characterization Theorem for a Modal Description Logic

Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality that can be understood as an epistemic operator or as representing (undirected) change. This logic embeds into a corresponding modal first-order logic S5-FOL. We prove a modal characterization theorem for this embedding, in analogy to results by van Benthem and Rosen relating ALC to standard first-order logic: We show that S5-ALC with only local roles is, both over finite and over unrestricted models, precisely the bisimulation invariant fragment of S5-FOL, thus giving an exact description of the expressive power of S5-ALC with only local roles

MACE 2.0 Reference Manual and Guide

MACE is a program that searches for finite models of first-order statements. The statement to be modeled is first translated to clauses, then to relational clauses; finally for the given domain size, the ground instances are constructed. A Davis-Putnam-Loveland-Logeman procedure decides the propositional problem, and any models found are translated to first-order models. MACE is a useful complement to the theorem prover Otter, with Otter searching for proofs and MACE looking for countermodels.Comment: 10 page

TDL--- A Type Description Language for Constraint-Based Grammars

This paper presents \tdl, a typed feature-based representation language and inference system. Type definitions in \tdl\ consist of type and feature constraints over the boolean connectives. \tdl\ supports open- and closed-world reasoning over types and allows for partitions and incompatible types. Working with partially as well as with fully expanded types is possible. Efficient reasoning in \tdl\ is accomplished through specialized modules.Comment: Will Appear in Proc. COLING-9

State space c-reductions for concurrent systems in rewriting logic

We present c-reductions, a state space reduction technique. The rough idea is to exploit some equivalence relation on states (possibly capturing system regularities) that preserves behavioral properties, and explore the induced quotient system. This is done by means of a canonizer function, which maps each state into a (non necessarily unique) canonical representative of its equivalence class. The approach exploits the expressiveness of rewriting logic and its realization in Maude to enjoy several advantages over similar approaches: exibility and simplicity in the definition of the reductions (supporting not only traditional symmetry reductions, but also name reuse and name abstraction); reasoning support for checking and proving correctness of the reductions; and automatization of the reduction infrastructure via Maude's meta-programming features. The approach has been validated over a set of representative case studies, exhibiting comparable results with respect to other tools

kLog: A Language for Logical and Relational Learning with Kernels

We introduce kLog, a novel approach to statistical relational learning. Unlike standard approaches, kLog does not represent a probability distribution directly. It is rather a language to perform kernel-based learning on expressive logical and relational representations. kLog allows users to specify learning problems declaratively. It builds on simple but powerful concepts: learning from interpretations, entity/relationship data modeling, logic programming, and deductive databases. Access by the kernel to the rich representation is mediated by a technique we call graphicalization: the relational representation is first transformed into a graph --- in particular, a grounded entity/relationship diagram. Subsequently, a choice of graph kernel defines the feature space. kLog supports mixed numerical and symbolic data, as well as background knowledge in the form of Prolog or Datalog programs as in inductive logic programming systems. The kLog framework can be applied to tackle the same range of tasks that has made statistical relational learning so popular, including classification, regression, multitask learning, and collective classification. We also report about empirical comparisons, showing that kLog can be either more accurate, or much faster at the same level of accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at http://klog.dinfo.unifi.it along with tutorials