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Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there…
Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…
A policy describes the conditions under which an action is permitted or forbidden. We show that a fragment of (multi-sorted) first-order logic can be used to represent and reason about policies. Because we use first-order logic, policies…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
We introduce Bifurcation Logic, BL, which combines a basic classical modality with separating conjunction * together with its naturally associated multiplicative implication, that is defined using the modal ordering. Specifically, a formula…
This work, shows how propositional resolution can be generalized to obtain a resolution proof system for constrained pseudo-propositional logic (CPPL), which is an extension resulted from inserting the natural numbers with few constraints…
The separability problem for word languages of a class $\mathcal{C}$ by languages of a class $\mathcal{S}$ asks, for two given languages $I$ and $E$ from $\mathcal{C}$, whether there exists a language $S$ from $\mathcal{S}$ that includes…
An important endeavor in computer science is to understand the expressive power of logical formalisms over discrete structures, such as words. Naturally, "understanding" is not a mathematical notion. This investigation requires therefore a…
The study of various decision problems for logic fragments has a long history in computer science. This paper is on the membership problem for a fragment of first-order logic over infinite words; the membership problem asks for a given…
Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper,…
We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…
The Univalent Foundations requires a logic that allows us to define structures on homotopy types, similar to how first-order logic with equality ($\text{FOL}_=$) allows us to define structures on sets. We develop the syntax, semantics and…
Term modal logics (TML) are modal logics with unboundedly many modalities, with quantification over modal indices, so that we can have formulas of the form $\exists y. \forall x. (\Box_x P(x,y) \supset\Diamond_y P(y,x))$. Like First order…
The regular languages with a neutral letter expressible in first-order logic with one alternation are characterized. Specifically, it is shown that if an arbitrary $\Sigma_2$ formula defines a regular language with a neutral letter, then…
We continue our study of open and closed languages. We investigate how the properties of being open and closed are preserved under concatenation. We investigate analogues, in formal languages, of the separation axioms in topological spaces;…
The interpolant existence problem (IEP) for a logic L is to decide, given formulas P and Q, whether there exists a formula I, built from the shared symbols of P and Q, such that P entails I and I entails Q in L. If L enjoys the Craig…
We introduce a high-level language with Python-like syntax for string-to-string, polyregular, first-order definable transductions. This language features function calls, boolean variables, and nested for-loops. We devise and implement a…
We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the…
We introduce an operator on classes of regular languages, the star-free closure. Our motivation is to generalize standard results of automata theory within a unified framework. Given an arbitrary input class $C$, the star-free closure…
Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational…