Related papers: Model Checking Existential Logic on Partially Orde…
Motivated by problems arising with the symbolic analysis of steady state ideals in Chemical Reaction Network Theory, we consider the problem of testing whether the points in a complex or real variety with non-zero coordinates form a coset…
A frame in an $n$-dimensional Hilbert space $H_n$ is a possibly redundant collection of vectors $\{f_i\}_{i\in I}$ that span the space. A tight frame is a generalization of an orthonormal basis. A frame $\{f_i\}_{i\in I}$ is said to be…
Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…
When an algebraic logic based on a poset instead of a lattice is investigated then there is a natural problem how to introduce the connective implication to be everywhere defined and satisfying (left) adjointness with the connective…
A monoid $M$ generated by a set $S$ of symbols can be described as the set of equivalence classes of finite words in $S$ under some relations that specify when some contiguous sequence of symbols can be replaced by another. If $a,b\in S$, a…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…
Probing experiments investigate the extent to which neural representations make properties -- like part-of-speech -- predictable. One suggests that a representation encodes a property if probing that representation produces higher accuracy…
Recently, the separated fragment (SF) of first-order logic has been introduced. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. SF properly generalizes both the…
We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is…
We continue our work on the model theory of free lattices, solving two of the main open problems from our first paper on the subject. Our main result is that the universal (existential) theory of infinite free lattices is decidable. Our…
Traditional language models treat language as a finite state automaton on a probability space over words. This is a very strong assumption when modeling something inherently complex such as language. In this paper, we challenge this by…
We define several sorts of mappings on a poset like monotone, strictly monotone, upper cone preserving and variants of these. Our aim is to characterize posets in which some of these mappings coincide. We define special mappings determined…
The characterization of the finite minimal automorphic posets of width three is still an open problem. Niederle has shown that this task can be reduced to the characterization of the nice sections of width three having a non-trivial tower…
Difference Logic (DL) is a fragment of linear arithmetics where atoms are constraints x+k <= y for variables x,y (ranging over Q or Z) and integer k. We study the complexity of deciding the truth of existential DL sentences. This problem…
We study the satisfiability problem for the two-variable first-order logic over structures with one transitive relation. % We show that the problem is decidable in 2-NExpTime for the fragment consisting of formulas where existential…
We prove that every finite poset has a directed cut with at least one half of the poset's pairwise order relations. The bound is tight. Also, the largest directed cut in a poset can be found in linear time.
We provide a constraint based computational model of linear precedence as employed in the HPSG grammar formalism. An extended feature logic which adds a wide range of constraints involving precedence is described. A sound, complete and…
Let $(X,\le)$ be a {\em non-empty strictly inductive poset}, that is, a non-empty partially ordered set such that every non-empty chain $Y$ has a least upper bound lub$(Y)\in X$, a chain being a subset of $X$ totally ordered by $\le$. We…
Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…
Suffixient sets are a novel prefix array (PA) compression technique based on subsampling PA (rather than compressing the entire array like previous techniques used to do): by storing very few entries of PA (in fact, a compressed number of…