Related papers: Intersection Logic in sequent calculus style
Following the idea of Subexponential Linear Logic and Stratified Bounded Linear Logic, we propose a new parameterized version of Linear Logic which subsumes other systems like ELL, LLL or SLL, by including variants of the exponential rules.…
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of…
This work contributes to the theory of judgment aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgment aggregation to cope with non-classical logics, we discuss in…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
In classical logic, "P implies Q" is equivalent to "not-P or Q". It is well known that the equivalence is problematic. Actually, from "P implies Q", "not-P or Q" can be inferred ("Implication-to-Disjunction" is valid), whereas from "not-P…
We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…
Formal representations of traffic scenarios can be used to generate test cases for the safety verification of autonomous driving. However, most existing methods are limited to highway or highly simplified intersection scenarios due to the…
Type isomorphism is useful for retrieving library components, since a function in a library can have a type different from, but isomorphic to, the one expected by the user. Moreover type isomorphism gives for free the coercion required to…
We add to intuitionistic logic infinitely many classical disjunctive tautologies and use the Curry--Howard correspondence to obtain typed concurrent $\lambda$-calculi; each of them features a specific communication mechanism, including…
Incorrectness Separation Logic (ISL) is a proof system designed to automate verification and detect bugs in programs manipulating heap memories. In this study, we extend ISL to support variable-length array predicates and pointer…
A central concept within informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their behaviour and properties. To this end, one requires an interpretation of logical formulae in terms of the…
We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract…
When sociologists and other social scientist ask whether the return to college differs by race and gender, they face a choice between two fundamentally different modes of inquiry. Traditional interaction models follow deductive logic: the…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
When comparing inductive logic programming (ILP) and attribute-value learning techniques, there is a trade-off between expressive power and efficiency. Inductive logic programming techniques are typically more expressive but also less…
We present new algorithm for computing the union and intersection of all justifications for a given ontological consequence without first computing the set of all justifications. Through an empirical evaluation, we show that our approach…
Within the program of finding axiomatizations for various parts of computability logic, it was proved earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort…
Two lines of approaches are adopted for complex reasoning with LLMs. One line of work prompts LLMs with various reasoning structures, while the structural outputs can be naturally regarded as intermediate reasoning steps. Another line of…
A cyclic proof system gives us another way of representing inductive definitions and efficient proof search. In 2011 Brotherston and Simpson conjectured the equivalence between the provability of the classical cyclic proof system and that…