Related papers: Two Results on Separation Logic With Theory Reason…

We study the problem of eliminating recursion from monadic datalog programs on trees with an infinite set of labels. We show that the boundedness problem, i.e., determining whether a datalog program is equivalent to some nonrecursive one is…

We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…

We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence…

Language models are often trained on text alone, without additional grounding. There is debate as to how much of natural language semantics can be inferred from such a procedure. We prove that entailment judgments between sentences can be…

We present in this paper a first-order axiomatization of an extended theory $T$ of finite or infinite trees, built on a signature containing an infinite set of function symbols and a relation $\fini(t)$ which enables to distinguish between…

We show that the problem `whether a finite set of regular-linear axioms defines a rigid theory' is undecidable.

The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…

A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…

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 paper establishes and proves complexity results for entailment for cumulative propositional dependence logic and for cumulative propositional logic with team semantics. As recently shown, cumulative logics are famously characterised by…

Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…

We consider the logic MSO+U, which is monadic second-order logic extended with the unbounding quantifier. The unbounding quantifier is used to say that a property of finite sets holds for sets of arbitrarily large size. We prove that the…

Termination of logic programs depends critically on the selection rule, i.e. the rule that determines which atom is selected in each resolution step. In this article, we classify programs (and queries) according to the selection rules for…

We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in…

Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without…

We prove that the isomorphism of scattered tree automatic linear orders as well as the existence of automorphisms of scattered word automatic linear orders are undecidable. For the existence of automatic automorphisms of word automatic…

The logic of bunched implications (BI), introduced by O'Hearn and Pym (1999), has attracted significant attention due to its elegant proof calculus, varied semantics, and close connections to the propositional fragment of separation logic.…

While there is a long tradition of reasoning about (non)termination in program analysis, specialized logics are typically needed to give different termination criteria. This includes partial correctness, where termination is not guaranteed,…