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Recently, it was shown that any theory of strings containing the string-replace function (even the most restricted version where pattern/replacement strings are both constant strings) becomes undecidable if we do not impose some kind of…
One of the most interesting questions concerning hierarchical control of discrete-event systems with partial observations is a condition under which the language observability is preserved between the original and the abstracted plant.…
A knowledge base is redundant if it contains parts that can be inferred from the rest of it. We study the problem of checking whether a CNF formula (a set of clauses) is redundant, that is, it contains clauses that can be derived from the…
The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…
Counting the number of answers to conjunctive queries is a fundamental problem in databases that, under standard assumptions, does not have an efficient solution. The issue is inherently #P-hard, extending even to classes of acyclic…
Inquisitive logic is a research program that extends the scope of logic to cover not only statements, but also questions. In the context of this program, a logic that plays a prominent role is inquisitive first-order logic, InqBQ, which…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
Several types of dependencies have been proposed for the static analysis of existential rule ontologies, promising insights about computational properties and possible practical uses of a given set of rules, e.g., in ontology-based query…
We propose a norm of consistency for a mixed set of defeasible and strict sentences, based on a probabilistic semantics. This norm establishes a clear distinction between knowledge bases depicting exceptions and those containing outright…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
Aiming to harmonise finite and infinite model reasoning, we initiate the study of partially finite models, where the reasoning task comes with a formula that specifies a part of the model that must be finite. We focus on the problem of…
Consistent Query Answering (CQA) is an inconsistency-tolerant approach to data access in knowledge bases and databases. The goal of CQA is to provide meaningful (consistent) answers to queries even in the presence of inconsistent…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…
In sequential functional languages, sized types enable termination checking of programs with complex patterns of recursion in the presence of mixed inductive-coinductive types. In this paper, we adapt sized types and their metatheory to the…
Metric Temporal Logic, $\mtlfull$ is amongst the most studied real-time logics. It exhibits considerable diversity in expressiveness and decidability properties based on the permitted set of modalities and the nature of time interval…
This paper addresses one of the fundamental open questions in the realm of existential rules: the conjecture on the finite controllability of bounded derivation depth rule sets (bdd $\Rightarrow$ fc). We take a step toward a positive…
On one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we divide…
Quantified modal logic provides a natural logical language for reasoning about modal attitudes even while retaining the richness of quantification for referring to predicates over domains. But then most fragments of the logic are…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…