Related papers: Four-valued logics of indicative conditionals
We introduce ologisms. They generate from ologs by extending their logical expressivity, from the possibility of considering constraints of equational nature only to the possibility of considering constraints of syllogistic nature, in…
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of…
We will extend the well-known Church encoding of Boolean logic into $\lambda$-calculus to an encoding of McCarthy's $3$-valued logic into a suitable infinitary extension of $\lambda$-calculus that identifies all unsolvables by $\bot$, where…
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…
In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that…
We investigate several categories related to transition structures, using a mixture of algebraic and topological methods. We show how two such categories are connected by a contravariant adjunction. This is the most detailed of a family of…
Drawing inferences between open-domain natural language predicates is a necessity for true language understanding. There has been much progress in unsupervised learning of entailment graphs for this purpose. We make three contributions: (1)…
We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other…
Although conventional logical systems based on logical calculi have been successfully used in mathematics and beyond, they have definite limitations that restrict their application in many cases. For instance, the principal condition for…
The thesis of this paper is that truth-relevant logic is a better foundation for mathematics than classical logic. It is a system proposed by Richard Diaz in 1981. In a certain sense t-relevant logic is based on Kleene strong tables. These…
We provide an in-depth study of tripartite entanglement of qudits. We start with a short review of tripartite entanglement invariants, prove a theorem about the complete list of all allowed values of three (out of the total of four) such…
We discuss the problem of defining a logic for analogical reasoning, and sketch a solution in the style of the semantics for Counterfactual Conditionals, Preferential Structures, etc.
The paper investigates from a proof-theoretic perspective various non-contractive logical systems circumventing logical and semantic paradoxes. Until recently, such systems only displayed additive quantifiers (Gri\v{s}in, Cantini). Systems…
This paper introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other approaches to this problem attempt to reproduce aspects of logical semantics within new…
We present a probabilistic extension of the description logic $\mathcal{ALC}$ for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
The paper proposes a new type of negation in multi-valued logics, providing a different way to answer the following question: what does it mean that some object language formula does not have a given truth-value. Along the way, the paper…
Linear-time computational techniques have been developed for combining evidence which is available on a number of contending hypotheses. They offer a means of making the computation-intensive calculations involved more efficient in certain…
The paper presents an extension of temporal epistemic logic with operators that quantify over strategies. The language also provides a natural way to represent what agents would know were they to be aware of the strategies being used by…
In this article, we study translations between variants of defaults logics such that the extensions of the theories that are the input and the output of the translation are in a bijective correspondence. We assume that a translation can…