Reconstructing a logic for inductive proofs of properties of functional programs

A logical framework consisting of a polymorphic call-by-value functional language and a first-order logic on the values is presented, which is a reconstruction of the logic of the verification system VeriFun. The reconstruction uses contextual semantics to define the logical value of equations. It equates undefinedness and non-termination, which is a standard semantical approach. The main results of this paper are: Meta-theorems about the globality of several classes of theorems in the logic, and proofs of global correctness of transformations and deduction rules. The deduction rules of VeriFun are globally correct if rules depending on termination are appropriately formulated. The reconstruction also gives hints on generalizations of the VeriFun framework: reasoning on nonterminating expressions and functions, mutual recursive functions and abstractions in the data values, and formulas with arbitrary quantifier prefix could be allowed

Towards Correctness of Program Transformations Through Unification and Critical Pair Computation

Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the combination of a context lemma with the computation of overlaps between program transformations and the reduction rules, and then of so-called complete sets of diagrams. The method is similar to the computation of critical pairs for the completion of term rewriting systems. We explore cases where the computation of these overlaps can be done in a first order way by variants of critical pair computation that use unification algorithms. As a case study we apply the method to a lambda calculus with recursive let-expressions and describe an effective unification algorithm to determine all overlaps of a set of transformations with all reduction rules. The unification algorithm employs many-sorted terms, the equational theory of left-commutativity modelling multi-sets, context variables of different kinds and a mechanism for compactly representing binding chains in recursive let-expressions.Comment: In Proceedings UNIF 2010, arXiv:1012.455

Computing overlappings by unification in the deterministic lambda calculus LR with letrec, case, constructors, seq and variable chains

Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the combination of a context lemma with the computation of overlaps between program transformations and the reduction rules.The method is similar to the computation of critical pairs for the completion of term rewriting systems. We describe an effective unification algorithm to determine all overlaps of transformations with reduction rules for the lambda calculus LR which comprises a recursive let-expressions, constructor applications, case expressions and a seq construct for strict evaluation. The unification algorithm employs many-sorted terms, the equational theory of left-commutativity modeling multi-sets, context variables of different kinds and a mechanism for compactly representing binding chains in recursive let-expressions. As a result the algorithm computes a finite set of overlappings for the reduction rules of the calculus LR that serve as a starting point to the automatization of the analysis of program transformations

SMILE: smart monitoring intelligent learning engine. An ontology-based context-aware system for supporting patients subjected to severe emergencies

Remote healthcare has made a revolution in the healthcare domain. However, an important problem this field is facing is supporting patients who are subjected to severe emergencies (as heart attacks) to be both monitored and protected while being at home. In this paper, we present a conceptual framework with the main objectives of: 1) emergency handling through monitoring patients, detecting emergencies and insuring fast emergency responses; 2) preventing an emergency from happening in the first place through protecting patients by organising their lifestyles and habits. To achieve these objectives, we propose a layered middleware. Our context model combines two modelling methods: probabilistic modelling to capture uncertain information and ontology to ease knowledge sharing and reuse. In addition, our system uses a two-level reasoning approach (ontology-based reasoning and Bayesian-based reasoning) to manage both certain and uncertain contextual parameters in an adaptive manner. Bayesian network is learned from ontology. Moreover, to ensure a more sophisticated decision-making for service presentation, influence diagram and analytic hierarchy process are used along with regular probabilistic rules (confidence level) and basic semantic logic rules

PRINCIPLES- AND RULES-BASED ACCOUNTING DEBATE. IMPLICATIONS FOR AN EMERGENT COUNTRY

By a qualitative analysis, this research observes whether a principles-based system or a mixed version of it with the rules-based system, applied in Romania - an emergent country - is appropriate taking into account the mentalities, the traditions, and other cultural elements that were typical of a rules-based system. We support the statement that, even if certain contextual variables are common to other developed countries, their environments significantly differ. To be effective, financial reporting must reflect the firm's context in which it is functioning. The research has a deductive approach based on the analysis of the cultural factors and their influence in the last years. For Romania it is argue a lower accounting professionalism associated with a low level of ambiguity tolerance. For the stage analysed in this study (after the year 2005) the professional reasoning - a proxy for the accounting professional behaviour - took into consideration the fiscal and legal requirements rather than the accounting principles and judgments. The research suggest that the Romanian accounting practice and the professionals are not fully prepared for a principles-based system environment, associated with the ability to find undisclosed events, facing ambiguity, identifying inferred relationships and using intuition, respectively working with uncertainty. We therefore reach the conclusion that in Romania institutional amendments affecting the professional expertise would be needed. The accounting regulations must be chosen with great caution and they must answer and/ or be adjusted, even if the process would be delayed, to national values, behaviour of companies and individual expertise and beliefs. Secondly, the benefits of applying accounting reasoning in this country may be enhanced through a better understanding of their content and through practical exercise. Here regulatory bodies may intervene for organizing professional training programs and acting towards the improvement of the codes of conduct's effectiveness.emergent countries, rules or principles-based system, IFRS

Machine ethics via logic programming

Machine ethics is an interdisciplinary field of inquiry that emerges from the need of imbuing autonomous agents with the capacity of moral decision-making. While some approaches provide implementations in Logic Programming (LP) systems, they have not exploited LP-based reasoning features that appear essential for moral reasoning. This PhD thesis aims at investigating further the appropriateness of LP, notably a combination of LP-based reasoning features, including techniques available in LP systems, to machine ethics. Moral facets, as studied in moral philosophy and psychology, that are amenable to computational modeling are identified, and mapped to appropriate LP concepts for representing and reasoning about them. The main contributions of the thesis are twofold. First, novel approaches are proposed for employing tabling in contextual abduction and updating – individually and combined – plus a LP approach of counterfactual reasoning; the latter being implemented on top of the aforementioned combined abduction and updating technique with tabling. They are all important to model various issues of the aforementioned moral facets. Second, a variety of LP-based reasoning features are applied to model the identified moral facets, through moral examples taken off-the-shelf from the morality literature. These applications include: (1) Modeling moral permissibility according to the Doctrines of Double Effect (DDE) and Triple Effect (DTE), demonstrating deontological and utilitarian judgments via integrity constraints (in abduction) and preferences over abductive scenarios; (2) Modeling moral reasoning under uncertainty of actions, via abduction and probabilistic LP; (3) Modeling moral updating (that allows other – possibly overriding – moral rules to be adopted by an agent, on top of those it currently follows) via the integration of tabling in contextual abduction and updating; and (4) Modeling moral permissibility and its justification via counterfactuals, where counterfactuals are used for formulating DDE.Fundação para a Ciência e a Tecnologia (FCT)-grant SFRH/BD/72795/2010 ; CENTRIA and DI/FCT/UNL for the supplementary fundin

Bilattice based Logical Reasoning for Automated Visual Surveillance and other Applications

The primary objective of an automated visual surveillance system is to observe and understand human behavior and report unusual or potentially dangerous activities/events in a timely manner. Automatically understanding human behavior from visual input, however, is a challenging task. The research presented in this thesis focuses on designing a reasoning framework that can combine, in a principled manner, high level contextual information with low level image processing primitives to interpret visual information. The primary motivation for this work has been to design a reasoning framework that draws heavily upon human like reasoning and reasons explicitly about visual as well as non-visual information to solve classification problems. Humans are adept at performing inference under uncertainty by combining evidence from multiple, noisy and often contradictory sources. This thesis describes a logical reasoning approach in which logical rules encode high level knowledge about the world and logical facts serve as input to the system from real world observations. The reasoning framework supports encoding of multiple rules for the same proposition, representing multiple lines of reasoning and also supports encoding of rules that infer explicit negation and thereby potentially contradictory information. Uncertainties are associated with both the logical rules that guide reasoning as well as with the input facts. This framework has been applied to visual surveillance problems such as human activity recognition, identity maintenance, and human detection. Finally, we have also applied it to the problem of collaborative filtering to predict movie ratings by explicitly reasoning about users preferences

A contextual behavioral approach to the study of (persecutory) delusions

Throughout the past century the topic of delusions has mainly been studied by researchers operating at the mental level of analysis. According to this perspective, delusional beliefs, as well as their emergence and persistence, stem from an interplay between (dysfunctional) mental representations and processes. Our paper aims to provide a starting point for researchers and clinicians interested in examining the topic of delusions from a functional-analytic perspective. We begin with a brief review of the research literature with a particular focus on persecutory delusions. Thereafter we introduce Contextual Behavioral Science (CBS), Relational Frame Theory (RFT) and a behavioral phenomenon known as arbitrarily applicable relational responding (AARR). Drawing upon AARR, and recent empirical developments within CBS, we argue that (persecutory) delusions may be conceptualized, studied and influenced using a functional-analytic approach. We consider future directions for research in this area as well as clinical interventions aimed at influencing delusions and their expression

Learning and Reasoning for Robot Sequential Decision Making under Uncertainty

Robots frequently face complex tasks that require more than one action, where sequential decision-making (SDM) capabilities become necessary. The key contribution of this work is a robot SDM framework, called LCORPP, that supports the simultaneous capabilities of supervised learning for passive state estimation, automated reasoning with declarative human knowledge, and planning under uncertainty toward achieving long-term goals. In particular, we use a hybrid reasoning paradigm to refine the state estimator, and provide informative priors for the probabilistic planner. In experiments, a mobile robot is tasked with estimating human intentions using their motion trajectories, declarative contextual knowledge, and human-robot interaction (dialog-based and motion-based). Results suggest that, in efficiency and accuracy, our framework performs better than its no-learning and no-reasoning counterparts in office environment.Comment: In proceedings of 34th AAAI conference on Artificial Intelligence, 202

Logical Step-Indexed Logical Relations

Appel and McAllester's "step-indexed" logical relations have proven to be a simple and effective technique for reasoning about programs in languages with semantically interesting types, such as general recursive types and general reference types. However, proofs using step-indexed models typically involve tedious, error-prone, and proof-obscuring step-index arithmetic, so it is important to develop clean, high-level, equational proof principles that avoid mention of step indices. In this paper, we show how to reason about binary step-indexed logical relations in an abstract and elegant way. Specifically, we define a logic LSLR, which is inspired by Plotkin and Abadi's logic for parametricity, but also supports recursively defined relations by means of the modal "later" operator from Appel, Melli\`es, Richards, and Vouillon's "very modal model" paper. We encode in LSLR a logical relation for reasoning relationally about programs in call-by-value System F extended with general recursive types. Using this logical relation, we derive a set of useful rules with which we can prove contextual equivalence and approximation results without counting steps