Related papers: Connecting Proof Theory and Knowledge Representati…
We introduce a type and effect system, for an imperative object calculus, which infers "sharing" possibly introduced by the evaluation of an expression, represented as an equivalence relation among its free variables. This direct…
We present a description of the PhD thesis which aims to propose a rule-based query answering method for relational data. In this approach we use an additional knowledge which is represented as a set of rules and describes the source data…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
Reversible computation is key in developing new, energy-efficient paradigms, but also in providing forward-only concepts with broader definitions and finer frames of study.Among other fields, the algebraic specification and representation…
The chase procedure for existential rules is an indispensable tool for several database applications, where its termination guarantees the decidability of these tasks. Most previous studies have focused on the skolem chase variant and its…
In many expert and everyday reasoning contexts it is very useful to reason on the basis of defeasible assumptions. For instance, if the information at hand is incomplete we often use plausible assumptions, or if the information is…
Propositional inquisitive logic is the limit of its $n$-bounded approximations. In the predicate setting, however, this does not hold anymore, as discovered by Ciardelli and Grilletti, who also found complete axiomatizations of $n$-bounded…
The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…
Diagram chasing is a customary proof method used in category theory and homological algebra. It involves an element-theoretic approach to show that certain properties hold for a commutative diagram. When dealing with abelian categories for…
Axiomatization has been widely used for testing logical implications. This paper suggests a non-axiomatic method, the chase, to test if a new dependency follows from a given set of probabilistic dependencies. Although the chase computation…
Reasoning with declarative knowledge (RDK) and sequential decision-making (SDM) are two key research areas in artificial intelligence. RDK methods reason with declarative domain knowledge, including commonsense knowledge, that is either…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
The chase is a ubiquitous algorithm in database theory. However, for existential rules (aka tuple-generating dependencies), its termination is not guaranteed, and even undecidable in general. The problem of termination becomes particularly…
We study the termination problem of the chase algorithm, a central tool in various database problems such as the constraint implication problem, Conjunctive Query optimization, rewriting queries using views, data exchange, and data…
We introduce a novel, logic-independent framework for the study of sequent-style proof systems, which covers a number of proof-theoretic formalisms and concrete proof systems that appear in the literature. In particular, we introduce a…
Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…
The connection method has earned good reputation in the area of automated theorem proving, due to its simplicity, efficiency and rational use of memory. This method has been applied recently in automatic provers that reason over ontologies…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…