Related papers: Nonclassical logics and multivariate truth values
Logicians study and apply a multiplicity of various logical systems. Consequently, there is necessity to build foundations and common grounds for all these systems. This is done in metalogic. Like metamathematics studies formalized…
Quantum logic understood as a reconstruction program had real successes and genuine limitations. This paper offers a synopsis of both and suggests a way of seeing quantum logic in a larger, still thriving context.
We discuss an ongoing line of research in the relational (non topological) semantics of non-distributive logics. The developments we consider are technically rooted in dual characterization results and insights from unified correspondence…
In this paper we consider the class of truth-functional many-valued logics with a finite set of truth-values. The main result of this paper is the development of a new \emph{binary} sequent calculi (each sequent is a pair of formulae) for…
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…
We introduce a variant of free logic (i.e., a logic admitting terms with nonexistent referents) that accommodates truth-value gluts as well as gaps. Employing a suitable expansion of the Belnap-Dunn four-valued logic, we specify a…
The difference between object-language and metalanguage is crucial for logical analysis, but has yet not been examined for the field of computer science. In this paper the difference is examined with regard to inferential relations. It is…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…
In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the…
To operate intelligently in the world, an agent must reason about its actions. The consequences of an action are a function of both the state of the world and the action itself. Many aspects of the world are inherently stochastic, so a…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…
Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning…
This chapter surveys some of the main results on interpolation in several of the most prominent families of non-classical logics. Special attention is given to the distinction between the two most commonly studied variants of…
The class of defeasible logics is only vaguely defined -- it is defined by a few exemplars and the general idea of efficient reasoning with defeasible rules. The recent definition of the defeasible logic $DL(\partial_{||})$ introduced new…
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…
Scholars have wondered for a long time whether the language of quantum mechanics introduces a quantum notion of truth which is formalized by quantum logic (QL) and is incompatible with the classical (Tarskian) notion. We show that QL can be…
Recent work in cognitive science has uncovered a diversity of explanatory values, or dimensions along which we judge explanations as better or worse. We propose a Bayesian account of how these values fit together to guide explanation. The…
We study many-valued coalgebraic logics with semi-primal algebras of truth-degrees. We provide a systematic way to lift endofunctors defined on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal…