Related papers: Cathoristic logic: A modal logic of incompatible p…

This paper presents a property of propositional theories under the answer sets semantics (called Equilibrium Logic for this general syntax): any theory can always be reexpressed as a strongly equivalent disjunctive logic program, possibly…

Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…

Posibilistic logic is the most extended approach to handle uncertain and partially inconsistent information. Regarding normal forms, advances in possibilistic reasoning are mostly focused on clausal form. Yet, the encoding of real-world…

The aim of this article is to generalize logics of formal inconsistency ($\textbf{LFI}$s) to systems dealing with the concept of incompatibility, expressed by means of a binary connective. The basic idea is that having two incompatible…

A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…

A recent proof, formulated in the symbolic language of modal logic, shows that a well-defined formulation of the possibility mentioned in the title is answered affirmatively. In the paper being commented upon several proposals were made…

Nominal logic is a variant of first-order logic that provides support for reasoning about bound names in abstract syntax. A key feature of nominal logic is the new-quantifier, which quantifies over fresh names (names not appearing in any…

Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-wise behaviour of a system. Its quantified extensions allow…

It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the…

This paper investigates the logical strength of completeness theorems for modal propositional logic within second-order arithmetic. We demonstrate that the weak completeness theorem for modal propositional logic is provable in…

Possibilistic logic is a well-known graded logic of uncertainty suitable to reason under incomplete information and partially inconsistent knowledge, which is built upon classical first order logic. There exists for Possibilistic logic a…

In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…

Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical…

Non-iterative normal modal logics are defined by axioms of modal degree 1. In this paper we use calculations with normal forms to determine the set of all possible non-iterative normal modal logics, unimodal propositional extensions of K.…

We present a procedure which allows us to recover classical and nonclassical logical structures as \emph{concrete logics} associated with physical theories expressed by means of classical languages. This procedure consists in choosing, for…

Scholars have wondered for a long time whether quantum mechanics (QM) subtends a quantum concept of truth which originates quantum logic (QL) and is radically different from the classical (Tarskian) concept of truth. We show in this paper…

Faroldi argues that deontic modals are hyperintensional and thus traditional modal logic cannot provide an appropriate formalization of deontic situations. To overcome this issue, we introduce novel justification logics as hyperintensional…

It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…

We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…

We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…