Related papers: Equational Reasoning Modulo Commutativity in Langu…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
I introduce modal group theory, in which we study the category of all groups, considering embeddability as providing a notion of modal possibility. Using HNN extensions and Britton's lemma, I demonstrate that the modal language of groups is…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
Natural language allows us to refer to novel composite concepts by combining expressions denoting their parts according to systematic rules, a property known as \emph{compositionality}. In this paper, we study whether the language emerging…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are…
I introduce renaming-enriched sets (rensets for short), which are algebraic structures axiomatizing fundamental properties of renaming (also known as variable-for-variable substitution) on syntax with bindings. Rensets compare favorably in…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in nondeterministic polynomial time. We also explore specializations like nominal letrec-matching for…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
The unification problem in a propositional logic is to determine, given a formula F, whether there exists a substitution s such that s(F) is in that logic. In that case, s is a unifier of F. When a unifiable formula has minimal complete…
We present a new approach to formal language theory using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate…
We develop a general model theoretic semantics to rewriting beyond the usual confluence and termination assumptions. This is based on preordered algebra which is a model theory that extends many sorted algebra. In this framework we…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
This paper proposes a modal typing system that enables us to handle self-referential formulae, including ones with negative self-references, which on one hand, would introduce a logical contradiction, namely Russell's paradox, in the…
Answer Set Programming Modulo Theories (ASPMT) is a new framework of tight integration of answer set programming (ASP) and satisfiability modulo theories (SMT). Similar to the relationship between first-order logic and SMT, it is based on a…
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…
We define an extension of the simply-typed lambda calculus where two different binding mechanisms, by position and by name, nicely coexist. In the former, as in standard lambda calculus, the matching between parameter and argument is done…
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…