Related papers: Intuitionistic Propositional Logic in Lean
The logic of bunched implication BI provides a framework for reasoning about resource composition and forms the basis for an assertion language of separation logic which is used to reason about software programs. Propositional BI is…
Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic…
This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…
In this paper, we have described a denotational model of Intuitionist Linear Logic which is also a differential category. Formulas are interpreted as Mackey-complete topological vector space and linear proofs are interpreted by bounded…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…
Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…
In this article, we add a diamond to the parametrized box-based propositional language of intuitionistic doxastic logic and intuitionistic epistemic logic introduced by Artemov and Protopopescu. The main results of this article are the…
We propose a new declarative planning language, called K, which is based on principles and methods of logic programming. In this language, transitions between states of knowledge can be described, rather than transitions between completely…
A common technique to verify complex logic specifications for dynamical systems is the construction of symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. Typically, abstractions…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
We investigate some finitely-valued generalizations of propositional dynamic logic with tests. We start by introducing the (n+1)-valued Kripke models and a corresponding language based on a modal extension of {\L}ukasiewicz many-valued…
This work contributes to the theory of judgment aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgment aggregation to cope with non-classical logics, we discuss in…
The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
Inspired by the efficient proof procedures discussed in {\em Computability logic} \cite{Jap03,Japic,Japfin}, we describe a heuristic proof procedure for first-order logic. This is a variant of Gentzen sequent system and has the following…
\textbf{T-BAT} logic is a formal system designed to express the notion of informal provability. This type of provability is closely related to mathematical practice and is quite often contrasted with formal provability, understood as a…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…