Related papers: First-Order Decomposition Trees
We introduce a model for the retrieval of information hidden in legal texts. These are typically organised in a hierarchical (tree) structure, which a reader interested in a given provision needs to explore down to the "deepest" level…
Algorithms for deriving Huffman codes and the recently developed algorithm for compiling PIFO trees to trees of fixed shape (Mohan et al. 2022) are similar, but work with different underlying algebraic operations. In this paper, we exploit…
Tree decompositions were developed by Robertson and Seymour. Since then algorithms have been developed to solve intractable problems efficiently for graphs of bounded treewidth. In this paper we extend tree decompositions to allow cycles to…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Several structure-learning algorithms for staged trees, asymmetric extensions of Bayesian networks, have been proposed. However, these either do not scale efficiently as the number of variables considered increases, a priori restrict the…
We provide elementary algorithms for two preservation theorems for first-order sentences (FO) on the class \^ad of all finite structures of degree at most d: For each FO-sentence that is preserved under extensions (homomorphisms) on \^ad, a…
Several theorems about the equivalence of familiar theories of reverse mathematics with certain well-ordering principles have been proved by recursion-theoretic and combinatorial methods (Friedman, Marcone, Montalban et al.) and with…
We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into…
We give the first data structure for the problem of maintaining a dynamic set of n elements drawn from a partially ordered universe described by a tree. We define the Line-Leaf Tree, a linear-sized data structure that supports the…
Let R^d -> A be a query problem over R^d for which there exists a data structure S that can compute P(q) in O(log n) time for any query point q in R^d. Let D be a probability measure over R^d representing a distribution of queries. We…
We study the problem of decomposing (clustering) a tree with respect to costs attributed to pairs of nodes, so as to minimize the sum of costs for those pairs of nodes that are in the same component (cluster). For the general case and for…
Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…
Recent language models enable new opportunities for structured reasoning with text, such as the construction of intuitive, proof-like textual entailment trees without relying on brittle formal logic. However, progress in this direction has…
An approach to clustering is presented that adapts the basic top-down induction of decision trees method towards clustering. To this aim, it employs the principles of instance based learning. The resulting methodology is implemented in the…
It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting…
We consider both analytically and numerically creation conditions of diverse hierarchical trees. A connection between the probabilities to create hierarchical levels and the probability to associate these levels into united structure is…
Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…
In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…
First-order logic is a natural way of expressing the properties of computation, traditionally used in various program logics for expressing the correctness properties and certificates. Subsequently, modern methods in the automated inference…
Bayesian networks are popular probabilistic models that capture the conditional dependencies among a set of variables. Inference in Bayesian networks is a fundamental task for answering probabilistic queries over a subset of variables in…