相关论文: Satisfaction classes in nonstandard models of firs…

An integer sequence is said to be 3-free if no three elements form an arithmetic progression. Following the greedy algorithm, the Stanley sequence $S(a_0,a_1,\ldots,a_k)$ is defined to be the 3-free sequence $\{a_n\}$ having initial terms…

Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those…

Machine learning enables systems to build and update domain models based on runtime observations. In this paper, we study statistical model checking and runtime verification for systems with this ability. Two challenges arise: (1) Models…

This thesis presents an alternative to Cantor's theory of cardinality, insofar as that is understood as a theory of set size. The alternative is based on a general theory, ClassSize. ClassSize contains all sentences in the first order…

To answer database queries over incomplete data the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their…

The so-called algebraic approach to the constraint satisfaction problem (CSP) has been a prevalent method of the study of complexity of these problems since early 2000's. The core of this approach is the notion of polymorphisms which…

We reformulate explanation quality assessment as a ranking problem rather than a generation problem. Instead of optimizing models to produce a single "best" explanation token-by-token, we train reward models to discriminate among multiple…

Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those…

A word $w$ is concise in a class of groups $\mathcal{C}$ if, for every group $G$ in $\mathcal{C}$, the verbal subgroup $w(G)$ is finite whenever $w$ takes only finitely many values in $G$. This notion can be naturally extended to…

Counterfactual explanations are a widely used approach in Explainable AI, offering actionable insights into decision-making by illustrating how small changes to input data can lead to different outcomes. Despite their importance, evaluating…

Let $\mathcal{L}$ be a first-order two-sorted language. Let $S$ be some fixed structure. A standard structure is an $\mathcal{L}$-structure of the form $(M,S)$, where $M$ is arbitrary. When $S$ is a compact topological space (and…

Classic supervised learning makes the closed-world assumption, meaning that classes seen in testing must have been seen in training. However, in the dynamic world, new or unseen class examples may appear constantly. A model working in such…

The class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that…

The identification and analysis of student satisfaction is a challenging issue. This is becoming increasingly important since a measure of student satisfaction is taken as an indication of how well a course has been taught. However, it…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

Clarithmetics are number theories based on computability logic (see http://www.csc.villanova.edu/~japaridz/CL/ ). Formulas of these theories represent interactive computational problems, and their "truth" is understood as existence of an…

Tarski's undefinability theorem states that a formal system based on conventional predicate logic (PL) cannot talk about its own truth predicate. PL is, however, not the only formal language imaginable. In this paper, it will be shown that…

First-order linear real arithmetic enriched with uninterpreted predicate symbols yields an interesting modeling language. However, satisfiability of such formulas is undecidable, even if we restrict the uninterpreted predicate symbols to…

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…

We prove that all standard subregular language classes are linearly separable when represented by their deciding predicates. This establishes finite observability and guarantees learnability with simple linear models. Synthetic experiments…