Related papers: Mutually Exclusive Modules in Logic Programming
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
We consider the one-shot Prisoner's Dilemma between algorithms with read-access to one anothers' source codes, and we use the modal logic of provability to build agents that can achieve mutual cooperation in a manner that is robust, in that…
Large Language Models (LLMs) have rapidly transformed the landscape of artificial intelligence, enabling natural language interfaces and dynamic orchestration of software components. However, their reliance on probabilistic inference limits…
Proof assistants play a dual role as programming languages and logical systems. As programming languages, proof assistants offer standard modularity mechanisms such as first-class functions, type polymorphism and modules. As logical…
In this chapter we study modal logics of topological spaces in the combined language with the derivational modality and the difference modality. We give axiomatizations and prove completeness for the following classes: all spaces,…
We present a Julia package, DisjunctiveProgramming.jl, that extends the functionality in JuMP.jl to allow modeling problems via logical propositions and disjunctive constraints. Such models can then be reformulated into Mixed-Integer…
Combining a set of existing constraint solvers into an integrated system of cooperating solvers is a useful and economic principle to solve hybrid constraint problems. In this paper we show that this approach can also be used to integrate…
Inductive Logic Programming (ILP) provides interpretable rule learning in relational domains, yet remains limited in its ability to induce and reason with numerical constraints. Classical ILP systems operate over discrete predicates and…
Functional programming comes in two flavours: one where ``functions are first-class citizens'' (we call this applicative) and one which is based on equations (we call this declarative). In relational programming clauses play the role of…
It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality. The idea is that of distributing the defeasible properties of concepts into different modules, according…
When programming resource-scarce embedded smart devices, the designer often requires both the low-level system programming features of a language such as C and higher level capability typical of a language like Java. The choice of a…
We investigate the expressive power of the two main kinds of program logics for complex, non-regular program properties found in the literature: those extending propositional dynamic logic (PDL), and those extending the modal mu-calculus.…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
We study a class of bilevel integer programs with second-order cone constraints at the upper level and a convex quadratic objective and linear constraints at the lower level. We develop disjunctive cuts to separate bilevel infeasible points…
Formally specifying, let alone verifying, properties of systems involving multiple programming languages is inherently challenging. We introduce Heterogeneous Dynamic Logic (HDL), a framework for combining reasoning principles from distinct…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…
Many important functional and security properties--including non-interference, determinism, and generalized non-interference (GNI)--are hyperproperties, i.e., properties relating multiple executions of a program. Existing separation logics…