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 Logic & Formal Reasoning


Guarantees for Real Robotic Systems: Unifying Formal Controller Synthesis and Reachset-Conformant Identification

arXiv.org Artificial Intelligence

Robots are used increasingly often in safety-critical scenarios, such as robotic surgery or human-robot interaction. To ensure stringent performance criteria, formal controller synthesis is a promising direction to guarantee that robots behave as desired. However, formally ensured properties only transfer to the real robot when the model is appropriate. We address this problem by combining the identification of a reachset-conformant model with controller synthesis. Since the reachset-conformant model contains all the measured behaviors of the real robot, the safety properties of the model transfer to the real robot. The transferability is demonstrated by experiments on a real robot, for which we synthesize tracking controllers.


From Probabilistic Programming to Complexity-based Programming

arXiv.org Artificial Intelligence

The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms proposed by Simplicity Theory, relying on the computation of two Kolmogorov complexities (here implemented as min-path searches via ASP programs) rather than probabilistic inference. The proposed system enables users to compute ex-post and ex-ante measures of unexpectedness of a certain situation, mapping respectively to posterior and prior subjective probabilities. The computation is based on the specification of world and mental models by means of causal and descriptive relations between predicates weighted by complexity. The paper illustrates a few examples of application: generating relevant descriptions, and providing alternative approaches to disjunction and to negation.


Strong-AI Autoepistemic Robots Build on Intensional First Order Logic

arXiv.org Artificial Intelligence

Neuro-symbolic AI attempts to integrate neural and symbolic architectures in a manner that addresses strengths and weaknesses of each, in a complementary fashion, in order to support robust strong AI capable of reasoning, learning, and cognitive modeling. In this paper we consider the intensional First Order Logic (IFOL) as a symbolic architecture of modern robots, able to use natural languages to communicate with humans and to reason about their own knowledge with self-reference and abstraction language property. We intend to obtain the grounding of robot's language by experience of how it uses its neuronal architectures and hence by associating this experience with the mining (sense) of non-defined language concepts (particulars/individuals and universals) in PRP (Properties/Relations/Propositions) theory of IFOL.\\ We consider the robot's four-levels knowledge structure: The syntax level of particular natural language (Italian, French, etc..), two universal language levels: its semantic logic structure (based on virtual predicates of FOL and logic connectives), and its corresponding conceptual PRP structure level which universally represents the composite mining of FOL formulae grounded on the last robot's neuro-system level. Finally, we provide the general method how to implement in IFOL (by using the abstracted terms) different kinds of modal logic operators and their deductive axioms: we present a particular example of robots autoepistemic deduction capabilities by introduction of the special temporal $Konow$ predicate and deductive axioms for it: reflexive, positive introspection and distributive axiom.


Womanhood is 'not a game of semantics,' attorney says after judge allows transgender sorority sister to remain

FOX News

A plaintiff in the lawsuit, Allie, and her lawyer Cassie Craven, join'America's Newsroom' to discuss the case, saying it is not about'trans inclusion,' but'erasing women.' Days after MSNBC interviewed transgender Wyoming sorority sister Artemis Langford following a judge's ruling in Langford's favor, a sorority sister and her attorney reacted on "America Reports." Artemis Langford, a transgender member of Kappa Kappa Gamma's University of Wyoming chapter, criticized media and public scrutiny received following the lawsuit, which was launched by several members of the college's chapter against the national sorority organization to bar Langford from membership. Federal Judge Alan Johnson, a Reagan appointee, ruled his court "will not define'woman' today," citing the lack of a definition of woman in KKG bylaws. The court cannot impede KKG's "freedom of expressive association," Johnson ruled.


Provably safe systems: the only path to controllable AGI

arXiv.org Artificial Intelligence

"Once the machine thinking method had started, it would not take long to outstrip our feeble powers. At some stage therefore we should have to expect the machines to take control" Alan Turing 1951 [35] AGI [91] safety is of the utmost urgency, since corporations and research labs are racing to build AGI despite prominent AI researchers and business leaders warning that it may lead to human extinction [11]. While governments are drafting AI regulations, there's little indication that they will be sufficient to resist competitive pressures and prevent the creation of AGI. Median estimates on the forecasting platform Metaculus of the date of AGI's creation have plummeted over the past few years from many decades away to 2027 [25] or 2032 [24] depending on definitions, with superintelligence expected to follow a few years later [23]. Is Alan Turing correct that we now "have to expect the machines to take control"?


Amortizing Pragmatic Program Synthesis with Rankings

arXiv.org Artificial Intelligence

In program synthesis, an intelligent system takes in a set of user-generated examples and returns a program that is logically consistent with these examples. The usage of Rational Speech Acts (RSA) framework has been successful in building \emph{pragmatic} program synthesizers that return programs which -- in addition to being logically consistent -- account for the fact that a user chooses their examples informatively. However, the computational burden of running the RSA algorithm has restricted the application of pragmatic program synthesis to domains with a small number of possible programs. This work presents a novel method of amortizing the RSA algorithm by leveraging a \emph{global pragmatic ranking} -- a single, total ordering of all the hypotheses. We prove that for a pragmatic synthesizer that uses a single demonstration, our global ranking method exactly replicates RSA's ranked responses. We further empirically show that global rankings effectively approximate the full pragmatic synthesizer in an online, multi-demonstration setting. Experiments on two program synthesis domains using our pragmatic ranking method resulted in orders of magnitudes of speed ups compared to the RSA synthesizer, while outperforming the standard, non-pragmatic synthesizer.


Declarative Reasoning on Explanations Using Constraint Logic Programming

arXiv.org Artificial Intelligence

Explaining opaque Machine Learning (ML) models is an increasingly relevant problem. Current explanation in AI (XAI) methods suffer several shortcomings, among others an insufficient incorporation of background knowledge, and a lack of abstraction and interactivity with the user. We propose REASONX, an explanation method based on Constraint Logic Programming (CLP). REASONX can provide declarative, interactive explanations for decision trees, which can be the ML models under analysis or global/local surrogate models of any black-box model. Users can express background or common sense knowledge using linear constraints and MILP optimization over features of factual and contrastive instances, and interact with the answer constraints at different levels of abstraction through constraint projection. We present here the architecture of REASONX, which consists of a Python layer, closer to the user, and a CLP layer. REASONX's core execution engine is a Prolog meta-program with declarative semantics in terms of logic theories.


Establishing trust in automated reasoning

arXiv.org Artificial Intelligence

Since its beginnings in the 1940s, automated reasoning by computers has become a tool of ever growing importance in scientific research. So far, the rules underlying automated reasoning have mainly been formulated by humans, in the form of program source code. Rules derived from large amounts of data, via machine learning techniques, are a complementary approach currently under intense development. The question of why we should trust these systems, and the results obtained with their help, has been discussed by philosophers of science but has so far received little attention by practitioners. The present work focuses on independent reviewing, an important source of trust in science, and identifies the characteristics of automated reasoning systems that affect their reviewability. It also discusses possible steps towards increasing reviewability and trustworthiness via a combination of technical and social measures.


Human Comprehensible Active Learning of Genome-Scale Metabolic Networks

arXiv.org Artificial Intelligence

An important application of Synthetic Biology is the engineering of the host cell system to yield useful products. However, an increase in the scale of the host system leads to huge design space and requires a large number of validation trials with high experimental costs. A comprehensible machine learning approach that efficiently explores the hypothesis space and guides experimental design is urgently needed for the Design-Build-Test-Learn (DBTL) cycle of the host cell system. We introduce a novel machine learning framework ILP-iML1515 based on Inductive Logic Programming (ILP) that performs abductive logical reasoning and actively learns from training examples. In contrast to numerical models, ILP-iML1515 is built on comprehensible logical representations of a genome-scale metabolic model and can update the model by learning new logical structures from auxotrophic mutant trials. The ILP-iML1515 framework 1) allows high-throughput simulations and 2) actively selects experiments that reduce the experimental cost of learning gene functions in comparison to randomly selected experiments.


On the Independencies Hidden in the Structure of a Probabilistic Logic Program

arXiv.org Artificial Intelligence

Pearl and Verma developed d-separation as a widely used graphical criterion to reason about the conditional independencies that are implied by the causal structure of a Bayesian network. As acyclic ground probabilistic logic programs correspond to Bayesian networks on their dependency graph, we can compute conditional independencies from d-separation in the latter. In the present paper, we generalize the reasoning above to the non-ground case. First, we abstract the notion of a probabilistic logic program away from external databases and probabilities to obtain so-called program structures. We then present a correct meta-interpreter that decides whether a certain conditional independence statement is implied by a program structure on a given external database. Finally, we give a fragment of program structures for which we obtain a completeness statement of our conditional independence oracle. We close with an experimental evaluation of our approach revealing that our meta-interpreter performs significantly faster than checking the definition of independence using exact inference in ProbLog 2.