580 research outputs found
Reasoning about Minimal Belief and Negation as Failure
We investigate the problem of reasoning in the propositional fragment of
MBNF, the logic of minimal belief and negation as failure introduced by
Lifschitz, which can be considered as a unifying framework for several
nonmonotonic formalisms, including default logic, autoepistemic logic,
circumscription, epistemic queries, and logic programming. We characterize the
complexity and provide algorithms for reasoning in propositional MBNF. In
particular, we show that entailment in propositional MBNF lies at the third
level of the polynomial hierarchy, hence it is harder than reasoning in all the
above mentioned propositional formalisms for nonmonotonic reasoning. We also
prove the exact correspondence between negation as failure in MBNF and negative
introspection in Moore's autoepistemic logic
Smart test data generators via logic programming
We present a novel counterexample generator for the interactive theorem prover Isabelle based on a compiler that synthesizes test data generators for functional programming languages (e.g. Standard ML, OCaml) from specifications in Isabelle. In contrast to naive type-based test data generators, the smart generators take the preconditions into account and only generate tests that fulfill the preconditions. The smart generators are constructed by a compiler that reformulates the preconditions as logic programs and analyzes them by an enriched mode inference. From this inference, the compiler can construct the desired generators in the functional programming language. These test data generators are applied to find errors in specifications, as we show in a case study of a hotel key card system
Learning to Find Proofs and Theorems by Learning to Refine Search Strategies: The Case of Loop Invariant Synthesis
We propose a new approach to automated theorem proving where an
AlphaZero-style agent is self-training to refine a generic high-level expert
strategy expressed as a nondeterministic program. An analogous teacher agent is
self-training to generate tasks of suitable relevance and difficulty for the
learner. This allows leveraging minimal amounts of domain knowledge to tackle
problems for which training data is unavailable or hard to synthesize. As a
specific illustration, we consider loop invariant synthesis for imperative
programs and use neural networks to refine both the teacher and solver
strategies
Towards the integration of functions, relations and types in an AI programming language
This paper describes the design and implementation of the programming language PC-Life. This language integrates the functional and the Logic-oriented programming style and feature types supporting inheritance. This combination yields a language particularly suited to knowledge representation, especially for application in computational linguistics
Transformers as Soft Reasoners over Language
Beginning with McCarthy's Advice Taker (1959), AI has pursued the goal of
providing a system with explicit, general knowledge and having the system
reason over that knowledge. However, expressing the knowledge in a formal
(logical or probabilistic) representation has been a major obstacle to this
research. This paper investigates a modern approach to this problem where the
facts and rules are provided as natural language sentences, thus bypassing a
formal representation. We train transformers to reason (or emulate reasoning)
over these sentences using synthetically generated data. Our models, that we
call RuleTakers, provide the first empirical demonstration that this kind of
soft reasoning over language is learnable, can achieve high (99%) accuracy, and
generalizes to test data requiring substantially deeper chaining than seen
during training (95%+ scores). We also demonstrate that the models transfer
well to two hand-authored rulebases, and to rulebases paraphrased into more
natural language. These findings are significant as it suggests a new role for
transformers, namely as limited "soft theorem provers" operating over explicit
theories in language. This in turn suggests new possibilities for
explainability, correctability, and counterfactual reasoning in
question-answering.Comment: IJCAI 202
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