This work focuses on data-parameterized abstract systems that extend standard modelling by allowing atomic propositions to be parameterized by variables that range over some infinite domain. These variables may range over process ids, message numbers, etc. Thus, abstract systems enable simple modelling of infinite-state systems whose source of infinity is the data. We define and study a simulat...

In this paper we show that relativized versions of relation set algebras and cylindric set algebras have undecidable equational theories if we include coordinatewise versions of the counting operations into the similarity type. We apply these results to the guarded fragment of first-order logic. ?

Grounding is the task of reducing a first-order theory and finite domain to an equivalent propositional theory. It is used as preprocessing phase in many logic-based reasoning systems. Such systems provide a rich first-order input language to a user and can rely on efficient propositional solvers to perform the actual reasoning. Besides a first-order theory and finite domain, the input for grou...

Providing a compositional interpretation procedure for discourses in which descriptions of complex dependencies between interrelated objects are incrementally built is a key challenge for formal theories of natural language interpretation. This paper examines several quantificational phenomena and argues that we need richly structured contexts of interpretation that are passed on between differ...

The efficiency of multi-relational data mining algorithms, addressing the problem of learning First Order Logic (FOL) theories, strongly depends on the search method used for exploring the hypotheses space and on the coverage test assessing the validity of the learned theory against the training examples. A way of tackling the complexity of this kind of learning systems is to use a propositiona...

Reiter’s default logic is supposed to reasoning on consistent knowledge; when inconsistencies or contradictions are present in a default theory, no useful conclusions can be extracted. In the past years, fragments and variants of the default logic are proposed to avoid or handle inconsistencies or contradictions. Unfortunately, the expressive and reasoning power of these fragments are strictly ...

The ability to reason about another person’s mental states, such as belief, desires and knowledge – first-order theory of mind – develops between the ages three and four. On the other hand, children need one or two more years to reason about a person who reasons about another person – secondorder theory of mind. Is it possible to accelerate the development of theory of mind? There are several t...

I explain a method to learn to achieve goals in games. In very complex games, such as the game of Go, a search intensive approach is intractable. A knowledge intensive approach is best suited. I represent knowledge using the combinatorial game theory and first order logic. I give a method to learn to predict the consequences of some moves. Each rule is learned using a single example, by explain...

We survey models and theories of geometric structures of parallelism, orthogonality, incidence, betweenness and order, thus gradually building towards full elementary geometry of Euclidean spaces, in Tarski’s sense. Besides the geometric aspects of such structures we look at their logical (first-order and modal) theories and discuss logical issues such as: expressiveness and definability, axiom...