Related papers: Model-theoretic characterization of intuitionistic…
We introduce a non-associative and non-commutative version of propositional intuitionistic linear logic, called propositional non-associative non-commutative intuitionistic linear logic (NACILL for short). We prove that NACILL and any of…
We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs. The system obtained this way resembles several known non-deterministic and algebraic lambda-calculi.
We present a framework for synthesising formulas in first-order logic (FOL) from examples, which unifies and advances state-of-the-art approaches for inference of transition system invariants. To do so, we study and categorise the existing…
Brotherston and Simpson [citation] have formalized and investigated cyclic reasoning, reaching the important conclusion that it is at least as powerful as inductive reasoning (specifically, they showed that each inductive proof can be…
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.…
In this paper we consider Modal Team Logic, a generalization of Classical Modal Logic in which it is possible to describe dependence phenomena between data. We prove that most known fragment of Full Modal Team Logic allow the elimination of…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
We consider a randomised version of Kleene's realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positive probability. In particular, we show that (i) the set of…
Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in…
It is known that intuitionistic Kripke semantics can be generalized so that it can treat arbitrary propositional connectives characterized by truth functions. We extend this generalized Kripke semantics to first-order logic, and study how…
Kaplan and Montague have showed that certain intuitive axioms for a first-order theory of knowledge, formalized as a predicate, are jointly inconsistent. Their arguments rely on self-referential formulas. I offer a consistent first-order…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We prove a generalization of Maehara's lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig's interpolation property. As a…
We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of…
Covariant-contravariant simulation is a combination of standard (covariant) simulation, its contravariant counterpart and bisimulation. We have previously studied its logical characterization by means of the covariant-contravariant modal…
One may formulate the dependent product types of Martin-L\"of type theory either in terms of abstraction and application operators like those for the lambda-calculus; or in terms of introduction and elimination rules like those for the…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
In computer science, various logical languages are defined to analyze properties of systems. One way to pinpoint the essential differences between those logics is to compare their expressivity in terms of distinguishing power and expressive…
An extension of the notion of dinatural transformation is introduced in order to give a criterion for preservation of dinaturality under composition. An example of an application is given by proving that all bicartesian closed canonical…