scholarly journals What’s Decidable About Program Verification Modulo Axioms?

2020 ◽  
pp. 158-177 ◽  
Author(s):  
Umang Mathur ◽  
P. Madhusudan ◽  
Mahesh Viswanathan
Keyword(s):  
Recent Work ◽  
Systematic Study ◽  
Program Verification ◽  
Total Order ◽  
First Order ◽  
Order Relations ◽  
Verification Problem

Abstract We consider the decidability of the verification problem of programs modulo axioms — automatically verifying whether programs satisfy their assertions, when the function and relation symbols are interpreted as arbitrary functions and relations that satisfy a set of first-order axioms. Though verification of uninterpreted programs (with no axioms) is already undecidable, a recent work introduced a subclass of coherent uninterpreted programs, and showed that they admit decidable verification [26]. We undertake a systematic study of various natural axioms for relations and functions, and study the decidability of the coherent verification problem. Axioms include relations being reflexive, symmetric, transitive, or total order relations, functions restricted to being associative, idempotent or commutative, and combinations of such axioms as well. Our comprehensive results unearth a rich landscape that shows that though several axiom classes admit decidability for coherent programs, coherence is not a panacea as several others continue to be undecidable.

scholarly journals VIII—Propositions and Cognitive Relations

2019 ◽  
Vol 119 (2) ◽  
pp. 157-178 ◽  
Author(s):  
Nicholas K Jones
Keyword(s):  
Natural Language ◽  
Recent Work ◽  
Natural Language Semantics ◽  
True Nature ◽  
First Order ◽  
Turn On ◽  
Language Semantics ◽  
Ontological Categories ◽  
The Difference ◽  
Semantic Types

Abstract There are two broad approaches to theorizing about ontological categories. Quineans use first-order quantifiers to generalize over entities of each category, whereas type theorists use quantification on variables of different semantic types to generalize over different categories. Does anything of import turn on the difference between these approaches? If so, are there good reasons to go type-theoretic? I argue for positive answers to both questions concerning the category of propositions. I also discuss two prominent arguments for a Quinean conception of propositions, concerning their role in natural language semantics and apparent quantification over propositions within natural language. It will emerge that even if these arguments are sound, there need be no deep question about Quinean propositions’ true nature, contrary to much recent work on the metaphysics of propositions.

Rotational line strengths in 3Δ–3Σ electronic transitions. The Herzberg III system of molecular oxygen

1986 ◽  
Vol 64 (1) ◽  
pp. 36-44 ◽  
Author(s):  
C. M. L. Kerr ◽  
J. K. G. Watson
Keyword(s):  
Molecular Oxygen ◽  
Satisfactory Agreement ◽  
Electronic Transitions ◽  
Rotational Line ◽  
Spin Orbit ◽  
First Order ◽  
Order Relations ◽  
Transition Moments ◽  
Wave Numbers ◽  
Line Strengths

Electronic transitions of the type 3Δ–3Σ are forbidden in the absence of spin–orbit or orbit–rotation coupling, but spin–orbit perturbations produce three transition moments, two perpendicular (Y1 and Y2) and one parallel (Z1) while low-order orbit–rotation couplings introduce three further perpendicular transition moments (X1, X2, and X3). Formulas are presented for the rotational line strengths in a 3Δ(a)–3Σ(int) transition in terms of these parameters and are applied to recent data of Coquart and Ramsay for the Herzberg III system [Formula: see text] of molecular oxygen. It is shown that all six parameters are significant, and that there are noticeable departures from the first-order relations Y1 = Y2, Z1 = 0, X1 = X2 = X3. The observation of orbit–rotation intensity effects led to the first identification of lines of the Ω′ = 3 subbands of the 4–0 to 7–0 bands of the Herzberg III system, which are forbidden for the spin–orbit mechanism. The wave numbers of these lines are in satisfactory agreement with the analysis of the A′3Δu → a1Δg emission by Slanger and Huestis.

Hybrid logics: characterization, interpolation and complexity

2001 ◽  
Vol 66 (3) ◽  
pp. 977-1010 ◽  
Author(s):  
Carlos Areces ◽  
Patrick Blackburn ◽  
Maarten Marx
Keyword(s):  
Recent Work ◽  
Order Logic ◽  
First Order Logic ◽  
Constrained System ◽  
First Order ◽  
Complexity Results

AbstractHybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called H(↓, @). We show in detail that (↓, @) is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations (via a restricted notion of Ehrenfeucht-Fraïssé game, and an enriched notion of bisimulation) and a syntactic characterization (in terms of bounded formulas). The key result to emerge is that (↓, @) corresponds to the fragment of first-order logic which is invariant for generated submodels. We then show that (↓, @) enjoys (strong) interpolation, provide counterexamples for its finite variable fragments, and show that weak interpolation holds for the sublanguage (@). Finally, we provide complexity results for (@) and other fragments and variants, and sharpen known undecidability results for (↓, @).

scholarly journals Partial and total order relations on a set

2021 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Knowledge Base ◽  
White Paper ◽  
Total Order ◽  
Order Relations

PARTIAL and TOTAL ORDER relations and their underlying definitions are presented in this white paper (knowledge base).

scholarly journals Learning Generalized Unsolvability Heuristics for Classical Planning

2021 ◽  
Author(s):  
Simon Ståhlberg ◽  
Guillem Francès ◽  
Jendrik Seipp
Keyword(s):  
Recent Work ◽  
Classification Accuracy ◽  
Supervised Classification ◽  
Learning Algorithms ◽  
Logical Form ◽  
Training Data ◽  
Goal State ◽  
Empirical Results ◽  
First Order ◽  
High Classification Accuracy

Recent work in classical planning has introduced dedicated techniques for detecting unsolvable states, i.e., states from which no goal state can be reached. We approach the problem from a generalized planning perspective and learn first-order-like formulas that characterize unsolvability for entire planning domains. We show how to cast the problem as a self-supervised classification task. Our training data is automatically generated and labeled by exhaustive exploration of small instances of each domain, and candidate features are automatically computed from the predicates used to define the domain. We investigate three learning algorithms with different properties and compare them to heuristics from the literature. Our empirical results show that our approach often captures important classes of unsolvable states with high classification accuracy. Additionally, the logical form of our heuristics makes them easy to interpret and reason about, and can be used to show that the characterizations learned in some domains capture exactly all unsolvable states of the domain.

scholarly journals Connecting Higher-Order Separation Logic to a First-Order Outside World

2020 ◽  
pp. 428-455 ◽  
Author(s):  
William Mansky ◽  
Wolf Honoré ◽  
Andrew W. Appel
Keyword(s):  
Program Verification ◽  
Higher Order ◽  
Separation Logic ◽  
C Programs ◽  
First Order ◽  
System Calls ◽  
Correctness Of Programs ◽  
Verified Software ◽  
Order State ◽  
Order Separation

AbstractSeparation logic is a useful tool for proving the correctness of programs that manipulate memory, especially when the model of memory includes higher-order state: Step-indexing, predicates in the heap, and higher-order ghost state have been used to reason about function pointers, data structure invariants, and complex concurrency patterns. On the other hand, the behavior of system features (e.g., operating systems) and the external world (e.g., communication between components) is usually specified using first-order formalisms. In principle, the soundness theorem of a separation logic is its interface with first-order theorems, but the soundness theorem may implicitly make assumptions about how other components are specified, limiting its use. In this paper, we show how to extend the higher-order separation logic of the Verified Software Toolchain to interface with a first-order verified operating system, in this case CertiKOS, that mediates its interaction with the outside world. The resulting system allows us to prove the correctness of C programs in separation logic based on the semantics of system calls implemented in CertiKOS. It also demonstrates that the combination of interaction trees + CompCert memories serves well as a lingua franca to interface and compose two quite different styles of program verification.

Individual differences in encoded semantic representations- PREPRINT

2020 ◽  
Author(s):  
Katherine L Alfred ◽  
Megan E Hillis ◽  
David J. M. Kraemer
Keyword(s):  
Individual Differences ◽  
General Relation ◽  
Semantic Distance ◽  
Semantic Representations ◽  
First Order ◽  
Order Relations ◽  
Semantic Concepts ◽  
Presentation Formats ◽  
Neural Mapping ◽  
Different Content

Semantic concepts relate to each other to varying degrees to form a network of first-order relations, and these first-order relations serve as input into networks of general relation types as well as higher order relations. Previous work has studied the neural mapping of semantic concepts across domains, though much work remains to be done to understand how the localization and structure of those architectures differ depending on various individual differences in attentional bias towards different content presentation formats. Using an item-wise model of semantic distance of first-order relations (word2vec) between stimuli (presented both in word and picture forms), we used representational similarity analysis to identify individual differences in the neural localization of semantic concepts, and how those localization differences can be predicted by individual variance in the degree to which individuals attend to word information instead of pictures. Importantly, there were no reliable representations of this first-order semantic relational network when looking at the full group, and it was only through considering individual differences that a stable localization difference became evident. These results indicate that individual differences in the degree to which a person habitually attends to word information instead of picture information substantially affects the neural localization of first-order semantic representations.

scholarly journals Attention to Configural Information in Change Detection for Faces

Perception ◽  
10.1068/p5517 ◽  
2007 ◽  
Vol 36 (9) ◽  
pp. 1353-1367 ◽  
Author(s):  
Simone K Favelle ◽  
Darren Burke
Keyword(s):  
Change Detection ◽  
Second Order ◽  
Object Discrimination ◽  
Attentional Allocation ◽  
Facial Region ◽  
First Order ◽  
Configural Information ◽  
Order Relations ◽  
Basic Level

In recent research the change-detection paradigm has been used along with cueing manipulations to show that more attention is allocated to the upper than lower facial region, and that this attentional allocation is disrupted by inversion. We report two experiments the object of which was to investigate how the type of information changed might be a factor in these findings by explicitly comparing the role of attention in detecting change to information thought to be ‘special’ to faces (second-order relations) with information that is more useful for basic-level object discrimination (first-order relations). Results suggest that attention is automatically directed to second-order relations in upright faces, but not first-order relations, and that this pattern of attentional allocation is similar across features.

scholarly journals AN EMPIRICAL EVALUATION OF AUTOMATED THEOREM PROVERS IN SOFTWARE CERTIFICATION

2006 ◽  
Vol 15 (01) ◽  
pp. 81-107 ◽  
Author(s):  
EWEN DENNEY ◽  
BERND FISCHER ◽  
JOHANN SCHUMANN
Keyword(s):  
System Architecture ◽  
High Performance ◽  
Program Verification ◽  
Source Code ◽  
Empirical Evaluation ◽  
Theorem Prover ◽  
Safety Properties ◽  
Proof Checking ◽  
First Order ◽  
The Individual

We describe a system for the automated certification of safety properties of NASA software. The system uses Hoare-style program verification technology to generate proof obligations which are then processed by an automated first-order theorem prover (ATP). We discuss the unique requirements this application places on the ATPs, focusing on automation, proof checking, traceability, and usability, and describe the resulting system architecture, including a certification browser that maintains and displays links between obligations and source code locations. For full automation, the obligations must be aggressively preprocessed and simplified, and we demonstrate how the individual simplification stages, which are implemented by rewriting, influence the ability of the ATPs to solve the proof tasks. Our results are based on 13 comprehensive certification experiments that lead to 366 top-level safety obligations and ultimately to more than 25,000 proof tasks which have been used to determine the suitability of the high-performance provers DCTP, E-Setheo, E, Gandalf, Otter, Setheo, Spass, and Vampire, and our associated infrastructure. The proofs found by Otter have been checked by Ivy.

From Stability to Simplicity

1998 ◽  
Vol 4 (1) ◽  
pp. 17-36 ◽  
Author(s):  
Byunghan Kim ◽  
Anand Pillay
Keyword(s):  
Recent Work ◽  
Stability Theory ◽  
Simple Theories ◽  
First Order ◽  
Closed Fields ◽  
Exhaustive Study ◽  
Pseudofinite Fields ◽  
Algebraically Closed Fields ◽  
Major Progress ◽  
Made In

§1. Introduction. In this report we wish to describe recent work on a class of first order theories first introduced by Shelah in [32], the simple theories. Major progress was made in the first author's doctoral thesis [17]. We will give a survey of this, as well as further works by the authors and others.The class of simple theories includes stable theories, but also many more, such as the theory of the random graph. Moreover, many of the theories of particular algebraic structures which have been studied recently (pseudofinite fields, algebraically closed fields with a generic automorphism, smoothly approximable structures) turn out to be simple. The interest is basically that a large amount of the machinery of stability theory, invented by Shelah, is valid in the broader class of simple theories. Stable theories will be defined formally in the next section. An exhaustive study of them is carried out in [33]. Without trying to read Shelah's mind, we feel comfortable in saying that the importance of stability for Shelah lay partly in the fact that an unstable theory T has 2λ many models in any cardinal λ ≥ ω1 + |T| (proved by Shelah). (Note that for λ ≥ |T| 2λ is the maximum possible number of models of cardinality λ.)

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