Related papers: A Binary Quantifier for Definite Descriptions for …
This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…
We apply Tatuzawa's version of Siegel's theorem to derive two lower bounds on the size of the principal genus of positive definite binary quadratic forms.
Query answering under existential rules -- implications with existential quantifiers in the head -- is known to be decidable when imposing restrictions on the rule bodies such as frontier-guardedness [BLM10, BLMS11]. Query answering is also…
In recent years, the effort to formalize erotetic inferences---i.e., inferences to and from questions---has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these…
We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$…
We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a…
A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…
We present a new syntactic criterion for the automatic detection of non-termination in an abstract setting that encompasses a simplified form of term rewriting and logic programming.
We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…
In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints ($\mathcal{L}_{\lvert\cdot\rvert}$) to a decision procedure for $\mathcal{L}_{\lvert\cdot\rvert}$ extended with set terms…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
In this paper we show that the intuitionistic theory for finitely many iterations of strictly positive operators is a conservative extension of the Heyting arithmetic. The proof is inspired by the quick cut-elimination due to G. Mints. This…
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…
We generalize the theory of stable canonical rules by adopting definable filtration, a generalization of the method of filtration. We show that for a modal rule system or a modal logic that admits definable filtration, each extension is…
For a group $G$, $\mathcal{F}_G$ denotes the set of all non-empty finite subsets of $G$. We extend the finitary coarse structure of $G$ from $G\times G$ to $\mathcal{F}_G\times \mathcal{F}_G$ and say that a macro-uniform mapping $f:…
We present the first verified implementation of a decision procedure for the quantifier-free theory of partial and linear orders. We formalise the procedure in Isabelle/HOL and provide a specification that is made executable using…
In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new…
Full first order linear logic can be presented as an abstract logic programming language in Miller's system Forum, which yields a sensible operational interpretation in the 'proof search as computation' paradigm. However, Forum still has to…