Related papers: Vagueness and the Connectives
Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…
We describe a natural deduction formalization of intuitionistic and classical propositional logic in the Isabelle/Pure framework. In contrast to earlier work, where we explored the pedagogical benefits of using a deep embedding approach to…
We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. We give an equivalent proof for the classical…
In the concluding remarks of Ontological Promiscuity Hobbs (1985) made what we believe to be a very insightful observation: given that semantics is an attempt at specifying the relation between language and the world, if "one can assume a…
In this paper, we present an alternative interpretation of propositional inquisitive logic as an epistemic logic of knowing how. In our setting, an inquisitive logic formula $\alpha$ being supported by a state is formalized as "knowing how…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Natural deduction systems, as proposed by Gentzen and further studied by Prawitz, is one of the most well known proof-theoretical frameworks. Part of its success is based on the fact that natural deduction rules present a simple…
Fast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically (ontologically) evolving systems one can still define a conserved quantum energy.…
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…
This paper studies the formation of logical operations from pre-logical processes. We are concerned with the reasons for certain mental processes taking form of logical reasoning and the underlying drives for consolidation of logical…
We revisit the issue of connections between two leading formalisms in nonmonotonic reasoning: autoepistemic logic and default logic. For each logic we develop a comprehensive semantic framework based on the notion of a belief pair. The set…
The one-variable fragment of a first-order logic may be viewed as an "S5-like" modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have…
We conjecture that the relative unpopularity of logical frameworks among practitioners is partly due to their complex meta-languages, which often demand both programming skills and theoretical knowledge of the meta-language in question for…
Quantum mechanics has been subject to logical scrutiny since its inception. The behavior of quantum systems, which are fundamentally dissimilar from classical systems, often appears to point to a logical inconsistency in quantum mechanics,…
The present paper proposes a new introductory treatment of the very well known Sahlqvist correspondence theory for classical modal logic. The first motivation for the present treatment is {\em pedagogical}: classical Sahlqvist…
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…
We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka…
It has recently been discovered that both quantum and classical propositional logics can be modelled by classes of non-orthomodular and thus non-distributive lattices that properly contain standard orthomodular and Boolean classes,…
Contingency and accident are two important notions in philosophy and philosophical logic. Their meanings are so close that they are mixed sometimes, in both everyday discourse and academic research. This indicates that it is necessary to…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…