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Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…
Standard answer set programming (ASP) targets at solving search problems from the first level of the polynomial time hierarchy (PH). Tackling search problems beyond NP using ASP is less straightforward. The class of disjunctive logic…
We look at classes of languages associated to the fragment of first-order logic B{\Sigma}1 which disallows quantifier alternations. Each class is defined by choosing the set of predicates on positions that may be used. Two key such…
Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…
Suppose X is the complex zero set of a finite collection of polynomials in Z[x_1,...,x_n]. We show that deciding whether X contains a point all of whose coordinates are d_th roots of unity can be done within NP^NP (relative to the sparse…
Hoare's logic is an axiomatic system of proving programs correct, which has been extended to be a separation logic to reason about mutable heap structure. We develop the most fundamental logical structure of strongest postcondition of…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assisted proofs and learning. The success of LP is traditionally…
We study the two-variable fragments D^2 and IF^2 of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D^2, both problems are…
We give a new characterization of elementary and deterministic polynomial time computation in linear logic through the proofs-as-programs correspondence. Girard's seminal results, concerning elementary and light linear logic, achieve this…
We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic entailment of the formulas, show its fixed-point…
Complex interval arithmetic is a powerful tool for the analysis of computational errors. The naturally arising rectangular, polar, and circular (together called primitive) interval types are not closed under simple arithmetic operations,…
When uncertainty meets costly information gathering, a fundamental question emerges: which data points should we probe to unlock near-optimal solutions? Sparsification of stochastic packing problems addresses this trade-off. The existing…
Let $b \ge 2$ be an integer. We prove that the $b$-adic expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms.…
Answer Set Programming (ASP) is a logic programming paradigm featuring a purely declarative language with comparatively high modeling capabilities. Indeed, ASP can model problems in NP in a compact and elegant way. However, modeling…
We give a quantifier elimination procedures for the extension of Presburger arithmetic with a unary threshold counting quantifier $\exists^{\ge c} y$ that determines whether the number of different $y$ satisfying some formula is at least $c…
Word equations are a crucial element in the theoretical foundation of constraint solving over strings. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant…
The Kochen-Specker no-go theorem established that hidden-variable theories in quantum mechanics necessarily admit contextuality. This theorem is formally stated in terms of the partial Boolean algebra structure of projectors on a Hilbert…
We give a number of approximation metatheorems for monotone maximization problems expressible in the first-order logic, in substantially more general settings than the previously known. We obtain * constant-factor approximation algorithm in…