Related papers: Display to Labeled Proofs and Back Again for Tense…
We use parsing as sequence labeling as a common framework to learn across constituency and dependency syntactic abstractions. To do so, we cast the problem as multitask learning (MTL). First, we show that adding a parsing paradigm as an…
We give examples of calculi that extend Gentzen's sequent calculus LK by unsound quantifier inferences in such a way that (i) derivations lead only to true sequents, and (ii) proofs therein are non-elementarily shorter than LK-proofs.
An Independent Parallelism Theorem is proven in the theory of adhesive HLR categories. It shows the bijective correspondence between sequential independent and parallel independent direct derivations in the Weak Double-Pushout framework,…
A proof procedure, in the spirit of the sequent calculus, is proposed to check the validity of entailments between Separation Logic formulas combining inductively defined predicates denoted structures of bounded tree width and theory…
Translating expressions between different logics and theorem provers is notoriously and often prohibitively difficult, due to the large differences between the logical foundations, the implementations of the systems, and the structure of…
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…
Pomset logic introduced by Retor\'e is an extension of linear logic with a self-dual noncommutative connective. The logic is defined by means of proof-nets, rather than a sequent calculus. Later a deep inference system BV was developed with…
We introduce a new Gentzen-style framework of grafted hypersequents that combines the formalism of nested sequents with that of hypersequents. To illustrate the potential of the framework, we present novel calculi for the modal logics…
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
Abstract separation logics are a family of extensions of Hoare logic for reasoning about programs that manipulate resources such as memory locations. These logics are "abstract" because they are independent of any particular concrete…
We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a…
We introduce the class of rational Kripke models and study symbolic model checking of the basic tense logic Kt and some extensions of it in models from that class. Rational Kripke models are based on (generally infinite) rational graphs,…
We study versions of Kleene algebra with dynamic tests, that is, extensions of Kleene algebra with domain and antidomain operators. We show that Kleene algebras with tests and Propositional dynamic logic correspond to special cases of the…
In this article, we explore the potential of transformer-based language models (LMs) to correctly represent normative statements in the legal domain, taking tax law as our use case. In our experiment, we use a variety of LMs as bases for…
Recently, prompt-based learning has gained popularity across many natural language processing (NLP) tasks by reformulating them into a cloze-style format to better align pre-trained language models (PLMs) with downstream tasks. However,…
Since the very beginning of the theory of linear logic it is known how to represent the $\lambda$-calculus as linear logic proof nets. The two systems however have different granularities, in particular proof nets have an explicit notion of…
We study the complexity and expressive power of conjunctive queries over unranked labeled trees represented using a variety of structure relations such as ``child'', ``descendant'', and ``following'' as well as unary relations for node…
Cyclic proof theory breaks tradition by allowing certain infinite proofs: those that can be represented by a finite graph, while satisfying a soundness condition. We reconcile cyclic proofs with traditional finite proofs: we extend abstract…
In a previous paper, a tableau calculus has been presented, which constitute a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work extends such a calculus to multi-modal…
Nested logic programs have recently been introduced in order to allow for arbitrarily nested formulas in the heads and the bodies of logic program rules under the answer sets semantics. Nested expressions can be formed using conjunction,…