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As instance of an overarching principle of exclusion an algorithm is presented that compactly (thus not one by one) generates all models of a Horn formula. The principle of exclusion can be adapted to generate only the models of weight $k$.…

The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…

This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. The special case of rational functions sharing the same…

We prove that all valid Herbrand equalities can be inter-procedurally inferred for programs where all assignments whose right-hand sides depend on at most one variable are taken into account. The analysis is based on procedure summaries…

Forgetting is an important concept in knowledge representation and automated reasoning with widespread applications across a number of disciplines. A standard forgetting operator, characterized in [Lin and Reiter'94] in terms of…

We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…

This paper places conformal testing in a general framework of statistical hypothesis testing. A standard approach to testing a composite null hypothesis $H$ is to test each of its elements and to reject $H$ when each of its elements is…

The problem of missing data, usually absent incurated and competition-standard datasets, is an unfortunate reality for most machine learning models used in industry applications. Recent work has focused on understanding the nature and the…

Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…

The Right to Explanation and the Right to be Forgotten are two important principles outlined to regulate algorithmic decision making and data usage in real-world applications. While the right to explanation allows individuals to request an…

We address the problem of checking the satisfiability of a set of constrained Horn clauses (CHCs) possibly including more than one query. We propose a transformation technique that takes as input a set of CHCs, including a set of queries,…

The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…

This paper investigates the problem of testing clause sets for membership in classes known from literature. In particular, we are interested in classes defined via renaming: Is it possible to rename the predicates in a way such that…

We investigate learnability of possibilistic theories from entailments in light of Angluin's exact learning model. We consider cases in which only membership, only equivalence, and both kinds of queries can be posed by the learner. We then…

Contrary to several other families of lambda terms, no closed formula or generating function is known and none of the sophisticated techniques devised in analytic combinatorics can currently help with counting or generating the set of {\em…

We consider a variation on the problem of prediction with expert advice, where new forecasters that were unknown until then may appear at each round. As often in prediction with expert advice, designing an algorithm that achieves…

Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…

We study nominal anti-unification, which is concerned with computing least general generalizations for given terms-in-context. In general, the problem does not have a least general solution, but if the set of atoms permitted in…

Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these…

Language models can be persuaded to abandon factual knowledge. This vulnerability is central to AI safety, but its internal mechanism remains poorly understood. We uncover a compact causal mechanism for persuasion-induced factual errors. A…