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Formal reasoning about finite sets and cardinality is an important tool for many applications, including software verification, where very often one needs to reason about the size of a given data structure and not only about what its…
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…
From an inconsistent database non-trivial arguments may be constructed both for a proposition, and for the contrary of that proposition. Therefore, inconsistency in a logical database causes uncertainty about which conclusions to accept.…
We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply…
We study word structures of the form $(D,<,P)$ where $D$ is either $\mathbb{N}$ or $\mathbb{Z}$, $<$ is the natural linear ordering on $D$ and $P\subseteq D$ is a predicate on $D$. In particular we show: (a) The set of recursive…
We know extensions of first order logic by quantifiers of the kind "there are uncountable many ...", "most ..." with new axioms and appropriate semantics. Related are operations such as "set of x, such that ...", Hilbert's…
A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical…
We study the problem of eliminating recursion from monadic datalog programs on trees with an infinite set of labels. We show that the boundedness problem, i.e., determining whether a datalog program is equivalent to some nonrecursive one is…
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…
Recent work by Faizal et al. (2025) claims that G\"odelian undecidability of non-algorithmic truths in our universe imply the impossibility of a formal, algorithmic simulation of the universe. This paper clarifies the distinction between…
We address the problem of supporting empirical probabilities in monadic logic databases. Though the semantics of multivalued logic programs has been studied extensively, the treatment of probabilities as results of statistical findings has…
Program logics typically reason about an over-approximation of program behaviour to prove the absence of bugs. Recently, program logics have been proposed that instead prove the presence of bugs by means of under-approximate reasoning,…
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of…
We propose a set of transformation rules for constraint logic programs with negation. We assume that every program is locally stratified and, thus, it has a unique perfect model. We give sufficient conditions which ensure that the proposed…
We propose the Transcendental Encoding Conjecture for decision problems, which asserts that every language in complexity class P encodes to an algebraic real (possibly rational or algebraic irrational) under its binary characteristic…
This paper describes a system, called PLP, for compiling ordered logic programs into standard logic programs under the answer set semantics. In an ordered logic program, rules are named by unique terms, and preferences among rules are given…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
We study the satisfiability problem for a modal logic expressing knowing-how assertions, which captures an agent's ability to achieve a given goal under the standard semantics based on linear plans. Our main result shows that satisfiability…