Reflection in conditional rewriting logic

AbstractWe recall general metalogical axioms for a reflective logic based on the notion of a universal theory, that is, a theory that can simulate the deductions of all other theories in a class of theories of interest, including itself. We then show that conditional rewriting logic is reflective, generalizing in two stages: first to the unsorted conditional case, and then to the many-sorted conditional case, the already known result for unconditional and unsorted rewriting logic (Reflection in Rewriting Logic: Metalogical Foundations and Metaprogramming Applications. CSLI Publications, 2000). This work should be seen as providing foundations for many useful applications of rewriting logic reflection. The results presented here have greatly influenced the design of the Maude language, which implements rewriting logic and supports its reflective capabilities, and have been used as a theoretical foundation for applications such as internal rewrite strategies, reflective design of theorem proving tools, module algebra and metaprogramming, and metareasoning in metalogical frameworks

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

The use of proof plans in tactic synthesis

We undertake a programme of tactic synthesis. We first formalize the notion of a tactic as a rewrite rule, then give a correctness criterion for this by means of a reflection mechanism in the constructive type theory OYSTER. We further formalize the notion of a tactic specification, given as a synthesis goal and a decidability goal. We use a proof planner. CIAM. to guide the search for inductive proofs of these, and are able to successfully synthesize several tactics in this fashion. This involves two extensions to existing methods: context-sensitive rewriting and higher-order wave rules. Further, we show that from a proof of the decidability goal one may compile to a Prolog program a pseudo- tactic which may be run to efficiently simulate the input/output behaviour of the synthetic tacti

Artificial general intelligence: Proceedings of the Second Conference on Artificial General Intelligence, AGI 2009, Arlington, Virginia, USA, March 6-9, 2009

Artificial General Intelligence (AGI) research focuses on the original and ultimate goal of AI – to create broad human-like and transhuman intelligence, by exploring all available paths, including theoretical and experimental computer science, cognitive science, neuroscience, and innovative interdisciplinary methodologies. Due to the difficulty of this task, for the last few decades the majority of AI researchers have focused on what has been called narrow AI – the production of AI systems displaying intelligence regarding specific, highly constrained tasks. In recent years, however, more and more researchers have recognized the necessity – and feasibility – of returning to the original goals of the field. Increasingly, there is a call for a transition back to confronting the more difficult issues of human level intelligence and more broadly artificial general intelligence