Related papers: Safe Formulas in the General Theory of Stable Mode…
Arguments about the safety, security, and correctness of a complex system are often made in the form of an assurance case. An assurance case is a structured argument, often represented with a graphical interface, that presents and supports…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
The definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a…
We survey the state-of-the-art on model-based formalisms for safety and security joint analysis, where safety refers to the absence of unintended failures, and security to absence of malicious attacks. We conduct a thorough literature…
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
Recent alignment studies commonly remove introductory boilerplate phrases from supervised fine-tuning (SFT) datasets. This work challenges that assumption. We hypothesize that safety- and reasoning-oriented prefix sentences serve as…
Hypothesis tests under order restrictions arise in a wide range of scientific applications. By exploiting inequality constraints, such tests can achieve substantial gains in power and interpretability. However, these gains come at a cost:…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…
Extensively evaluating the capabilities of (large) language models is difficult. Rapid development of state-of-the-art models induce benchmark saturation, while creating more challenging datasets is labor-intensive. Inspired by the recent…
The Smodels system implements the stable model semantics for normal logic programs. It handles a subclass of programs which contain no function symbols and are domain-restricted but supports extensions including built-in functions as well…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
Notions of asimulation and k-asimulation introduced in [Olkhovikov, 2011] are extended onto the level of predicate logic. We then prove that a first-order formula is equivalent to a standard translation of an intuitionistic predicate…
Recent work has shown that a model's input word embeddings can serve as effective control variables for steering its behavior toward outputs that satisfy desired properties. However, this has only been demonstrated for pretrained…
The paper that introduced shape analysis sentences presented a method for extracting a sentence in first-order logic that completely characterizes a run of CPSA. Logical deduction can then be used to determine if a security goal is…
In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First Order Logic is equivalent to some first order sentence. In this work it is shown that all…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely)…