Related papers: On the Count of Trees
We study the model-checking problem for recursion schemes: does the tree generated by a given higher-order recursion scheme satisfy a given logical sentence. The problem is known to be decidable for sentences of the MSO logic. We prove…
The grammar representation of a narrowing tree for a syntactically deterministic conditional term rewriting system and a pair of terms is a regular tree grammar that generates expressions for substitutions obtained by all possible…
This paper introduces derivation trees for general grammars. Within these trees, it defines context-dependent pairs of nodes, corresponding to rewriting two neighboring symbols using a non context-free rule. It proves that the language…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
Given a document D in the form of an unordered node-labeled tree, we study the expressiveness on D of various basic fragments of XPath, the core navigational language on XML documents. Working from the perspective of these languages as…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
Extending the popular Answer Set Programming (ASP) paradigm by introspective reasoning capacities has received increasing interest within the last years. Particular attention is given to the formalism of epistemic logic programs (ELPs)…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning…
Decision trees are widely used for interpretable machine learning due to their clearly structured reasoning process. However, this structure belies a challenge we refer to as predictive equivalence: a given tree's decision boundary can be…
We use the algebraic framework for languages of infinite trees introduced in [4] to derive effective characterisations of various temporal logics, in particular the logic EF (a fragment of CTL) and its counting variant cEF.
Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…
We consider an infinite sequence of rooted trees naturally emerging in a number-theoretical context. We advance some ideas on its structure by discussing some elementary properties. Some of those properties are shown to be related to…
Complex reasoning over text requires understanding and chaining together free-form predicates and logical connectives. Prior work has largely tried to do this either symbolically or with black-box transformers. We present a middle ground…
We introduce and study single-conclusioned nested sequent calculi for a broad class of intuitionistic multi-modal logics known as "intuitionistic grammar logics (IGLs)." These logics serve as the intuitionistic counterparts of classical…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…
Despite their remarkable capabilities, large language models often struggle with tasks requiring complex reasoning and planning. While existing approaches like Chain-of-Thought prompting and tree search techniques show promise, they are…