Related papers: A Sequent Calculus for Dynamic Topological Logic
We introduce labelled sequent calculi for the basic normal non-distributive modal logic L and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order language which is interpreted on the canonical extensions of…
Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We…
Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…
This thesis describes the theoretical and practical foundations of a system for the static analysis of XML processing languages. The system relies on a fixpoint temporal logic with converse, derived from the mu-calculus, where models are…
Justification logics are an explication of modal logic; boxes are replaced with proof terms formally through realisation theorems. This can be achieved syntactically using a cut-free proof system e.g. using sequent, hypersequent or nested…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
We introduce sound and complete labelled sequent calculi for the basic normal non-distributive modal logic L and some of its axiomatic extensions, where the labels are atomic formulas of the first order language of enriched formal contexts,…
In this paper, we integrate separation logic with Propositional Projection Temporal Logic (PPTL) to obtain a two-dimensional logic, namely PPTL$^{\tiny\mbox{SL}}$. The spatial dimension is realized by a decidable fragment of separation…
Quantified CTL (QCTL) is a well-studied temporal logic that extends CTL with quantification over atomic propositions. It has recently come to the fore as a powerful intermediary framework to study logics for strategic reasoning. We extend…
Dynamic HoTT (DHoTT) is a conservative extension of Homotopy Type Theory designed for evolving texts in conversational AI. In a chat system, a large language model (LLM) is queried with a growing prefix: at turn tau the input is C(tau), the…
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…
As an attempt to uncover the topological nature of composition of strategies in game semantics, we present a ``topological'' game for Multiplicative Additive Linear Logic without propositional variables, including cut moves. We recast the…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…
We design hypersequent calculus proof systems for the theories of Riesz spaces and modal Riesz spaces and prove the key theorems: soundness, completeness and cut elimination. These are then used to obtain completely syntactic proofs of some…
Formal mathematics and computer science proofs are formalized using Hilbert-Russell-style logical systems which are designed to not admit paradoxes and self-refencing reasoning. These logical systems are natural way to describe and reason…
This paper introduces operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
Temporal logics are an obvious high-level descriptive companion formalism to dynamical systems which model behavior as deterministic evolution of state over time. A wide variety of distinct temporal logics applicable to dynamical systems…