Related papers: First-Order and Temporal Logics for Nested Words
This paper studies nested sequents for quantified modal logics. In particular, it considers extensions of the propositional modal logics definable by the axioms D, T, B, 4, and 5 with varying, increasing, decreasing, and constant domains.…
We study an extension of $\mtl$ in pointwise time with rational expression guarded modality $\reg_I(\re)$ where $\re$ is a rational expression over subformulae. We study the decidability and expressiveness of this extension ($\mtl$+$\varphi…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
We introduce a new hierarchy of higher-order nested pushdown trees generalising Alur et al.'s concept of nested pushdown trees. Nested pushdown trees are useful representations of control flows in the verification of programs with recursive…
Temporal logics over finite traces are not the same as temporal logics over potentially infinite traces. Ro\c{s}u first proved completeness for linear temporal logic on finite traces (LTLf) with a novel coinductive axiom. We offer a…
Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) extend Linear Temporal Logic (LTL) for real-time constraints, with MTL using time-bounded modalities and TPTL employing freeze quantifiers. Satisfiability for both is…
We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is…
TMs are a pattern recognition approach that uses finite state machines for learning and propositional logic to represent patterns. In addition to being natively interpretable, they have provided competitive accuracy for various tasks. In…
We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…
Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…
Translating formal language into natural language is a foundational challenge in NLP, driving various downstream applications in semantic parsing, theorem validation, and question answering. In this study, we introduce First-Order Logic to…
This article examines the interpretation of the LTL temporal operators over finite and infinite sequences. This is used as the basis for deriving a sound and complete axiomatization for Caret, a recent temporal logic for reasoning about…
Metric Temporal Logic, $\mtlfull$ is amongst the most studied real-time logics. It exhibits considerable diversity in expressiveness and decidability properties based on the permitted set of modalities and the nature of time interval…
Modular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We…
The Triguarded Fragment (TGF) is among the most expressive decidable fragments of first-order logic, subsuming both its two-variable and guarded fragments without equality. We show that the TGF has the finite model property (providing a…
We characterise non-distributive positive logic as the fragment of a single-sorted first-order language that is preserved by a new notion of simulation called a meet-simulation. Meet-simulations distinguish themselves from simulations…
In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized model-checking problems for various fragments of first-order…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
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 study the generalization abilities of language models when translating natural language into formal specifications with complex semantics. In particular, we fine-tune language models on three datasets consisting of English sentences and…