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We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
One version of the concept of structural controllability defined for single-input systems by Lin and subsequently generalized to multi-input systems by others, states that a parameterized matrix pair $(A, B)$ whose nonzero entries are…
Multidimensional contractions of irreducible representations of the Cayley-Klein unitary algebras in the Gel'fand-Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method…
The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…
This article is concerned with automated complexity analysis of term rewrite systems. Since these systems underlie much of declarative programming, time complexity of functions defined by rewrite systems is of particular interest. Among…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
Dependencies have played a significant role in database design for many years. They have also been shown to be useful in query optimization. In this paper, we discuss dependencies between lexicographically ordered sets of tuples. We…
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…
A prevailing assumption in machine learning is that model correctness must be enforced after the fact. We observe that the properties determining whether an AI model is numerically stable, computationally correct, or consistent with a…
Dependency parsing is a fundamental task in natural language processing (NLP), aiming to identify syntactic dependencies and construct a syntactic tree for a given sentence. Traditional dependency parsing models typically construct…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
In the article the problem of the integrable classification of nonlinear lattices depending on one discrete and two continuous variables is studied. By integrability we mean the presence of reductions of a chain to a system of hyperbolic…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Current machine learning models are evaluated through behavioral snapshots, with benchmark accuracies, win rates and outcome-based metrics. Model explanations and evaluations, however, are fundamentally intertwined: understanding why a…
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
Following the types-as-sets paradigm, we present a mechanized embedding of dependent function types with a hierarchy of universes into schematic first-order logic with equality, with axiom schemas of Tarski-Grothendieck set theory. We carry…
The static dependency pair method is a method for proving the termination of higher-order rewrite systems a la Nipkow. It combines the dependency pair method introduced for first-order rewrite systems with the notion of strong computability…
Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…
We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…