Related papers: First-order answer set programming as constructive…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…
The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic…
In many probabilistic first-order representation systems, inference is performed by "grounding"---i.e., mapping it to a propositional representation, and then performing propositional inference. With a large database of facts, groundings…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
The first-order theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary first-order theories. We prove that the first-order theory of a string automatic…
Answer Set Programming (ASP) is a logic-based knowledge representation framework, supporting---among other reasoning modes---the central task of query answering. In the propositional case, query answering amounts to computing cautious…
We provide a comprehensive elaboration of the theoretical foundations of variable instantiation, or grounding, in Answer Set Programming (ASP). Building on the semantics of ASP's modeling language, we introduce a formal characterization of…
Liveness properties are traditionally proven using a ranking function that maps system states to some well-founded set. Carrying out such proofs in first-order logic enables automation by SMT solvers. However, reasoning about many natural…
The description complexity of a model is the length of the shortest formula that defines the model. We study the description complexity of unary structures in first-order logic FO, also drawing links to semantic complexity in the form of…
A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs.…
We investigate mca-programs, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a non-negative integer and X is a finite set of propositional atoms. We develop a theory of mca-programs. We…
In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category…
This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…
Robots assisting humans in complex domains have to represent knowledge and reason at both the sensorimotor level and the social level. The architecture described in this paper couples the non-monotonic logical reasoning capabilities of a…
We consider a declarative framework for machine learning where concepts and hypotheses are defined by formulas of a logic over some background structure. We show that within this framework, concepts defined by first-order formulas over a…
We show that the classical interpretations of Tarski's inductive definitions actually allow us to define the satisfaction and truth of the quantified formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers…
Decision tree models, including random forests and gradient-boosted decision trees, are widely used in machine learning due to their high predictive performance. However, their complex structures often make them difficult to interpret,…
We introduce first order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first order formulae, with states and internal variables given by uninterpreted…
Full first order linear logic can be presented as an abstract logic programming language in Miller's system Forum, which yields a sensible operational interpretation in the 'proof search as computation' paradigm. However, Forum still has to…