Soundness Research Articles

In search of doxastic involuntarism

Doxastic involuntarists, as I categorize them, say that it’s impossible to form a belief as an intentional action. But what exactly is it to form a belief, as opposed to simply getting yourself to have one? (Everyone agrees you could do that intentionally.) This question has been insufficiently addressed, and the lacuna threatens the involuntarists’ position: if the question isn’t answered, their view will lack any clear content; but, after considering some straightforward ways of answering it, I argue that they would make involuntarism either false or insignificant. I also examine several involuntarist arguments, and find them faltering at just this point: inadequate attention to belief-formation results in unsound arguments or insignificant conclusions. The viability of involuntarism as a meaningful position, I conclude, turns on whether the notion of belief-formation can be further developed.

Skeptical Arguments and Deep Disagreement

This paper provides a reinterpretation of some of the most influential skeptical arguments, Agrippa’s trilemma, meta-regress arguments, and Cartesian external world skepticism. These skeptical arguments are reasonably regarded as unsound arguments about the extent of our knowledge. However, reinterpretations of these arguments tell us something significant about the preconditions and limits of persuasive argumentation. These results contribute to the ongoing debates about the nature and resolvability of deep disagreement. The variety of skeptical arguments shows that we must distinguish different types of deep disagreement. Moreover, the reinterpretation of skeptical arguments elucidates that deep disagreement cannot be resolved via argumentation.

A Finitely Axiomatized Non-Classical First-Order Theory Incorporating Category Theory and Axiomatic Set Theory

It is well known that Zermelo-Fraenkel Set Theory (ZF), despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely many axioms, and it has a countable model due to the Löwenheim–Skolem theorem. This paper presents the axioms one has to accept to get rid of these two features. For that matter, some twenty axioms are formulated in a non-classical first-order language with countably many constants: to this collection of axioms is associated a universe of discourse consisting of a class of objects, each of which is a set, and a class of arrows, each of which is a function. The axioms of ZF are derived from this finite axiom schema, and it is shown that it does not have a countable model—if it has a model at all, that is. Furthermore, the axioms of category theory are proven to hold: the present universe may therefore serve as an ontological basis for category theory. However, it has not been investigated whether any of the soundness and completeness properties hold for the present theory: the inevitable conclusion is therefore that only further research can establish whether the present results indeed constitute an advancement in the foundations of mathematics.

First-order logic as a constraint satisfaction problem

In this paper, we discourse an analysis of classical first-order predicate logic as a constraint satisfaction problem, CSP. First, we will offer our general framework for CSPs, and then apply it to first-order logic. We claim it would function as a new semantics, constraint semantics, for logic. Then, we prove the soundness and completeness theorems with respect to the constraint semantics. The latter theorem, which will be proven by a proof-search method, implies the cut-elimination theorem. Furthermore, using the constraint semantics, we make a new proof of the Craig interpolation theorem. Also, we will provide feasible algorithms to generate interpolants for some decidable fragments of first-order logic: the propositional logic and the monadic fragments. The algorithms, reflecting a ‘projection’ of an indexed relation, will show how to transform given formulas syntactically to obtain interpolants.

A dependently typed calculus with polymorphic subtyping

• A dependently-typed language that features implicit polymorphism, general recursion and explicit type-level computation. • Higher ranked subtype reasoning about the more-general-than relation between polymorphic types. • Fully mechanized proof of the type soundness and transitivity. A polymorphic subtyping relation, which relates more general types to more specific ones, is at the core of many modern functional languages. As those languages start moving towards dependently typed programming a natural question is how can polymorphic subtyping be adapted to such settings. This paper presents the dependent implicitly polymorphic calculus ( λ I ∀ ): a simple dependently typed calculus with polymorphic subtyping. The subtyping relation in λ I ∀ generalizes the well-known polymorphic subtyping relation by Odersky and Läufer (1996). Because λ I ∀ is dependently typed, integrating subtyping in the calculus is non-trivial. To overcome many of the issues arising from integrating subtyping with dependent types, the calculus employs unified subtyping , which is a technique that unifies typing and subtyping into a single relation. Moreover, λ I ∀ employs explicit casts instead of a conversion rule, allowing unrestricted recursion to be naturally supported. We prove various non-trivial results, including type soundness and transitivity of unified subtyping. λ I ∀ and all corresponding proofs are mechanized in the Coq theorem prover.

Revisiting NIZK-Based Technique for Chosen-Ciphertext Security: Security Analysis and Corrected Proofs

Non-interactive zero-knowledge (NIZK) proofs for chosen-ciphertext security are generally considered to give an impractical construction. An interesting recent work by Seo, Abdalla, Lee, and Park (Information Sciences, July 2019) proposed an efficient semi-generic conversion method for achieving chosen-ciphertext security based on NIZK proofs in the random oracle model. The recent work by Seo et al. demonstrated that the semi-generic conversion method transforms a one-way (OW)-secure key encapsulation mechanism (KEM) into a chosen-ciphertext secure KEM while preserving tight security reduction. This paper shows that the security analysis of the semi-generic conversion method has a flaw, which comes from the OW security condition of the underlying KEM. Without changing the conversion method, this paper presents a revised security proof under the changed conditions that (1) the underlying KEM must be chosen-plaintext secure in terms of indistinguishability and (2) an NIZK proof derived from the underlying KEM via the Fiat–Shamir transform must have the properties of zero-knowledge and simulation soundness. This work extended the security proof strategy to the case of identity-based KEM (IBKEM) and also revise the security proof for IBKEM of previous method by Seo et al. Finally, this work gives a corrected security proof by applying the new proofs to several existing (IB)KEMs.

High-throughput investigation of laser powder bed fabricated Inconel 718 alloy: Fabrication, microstructure and performance

Additive manufacturing provides a possibility to realize high throughput investigation of material preparation and processing. In order to thoroughly investigate the effect of the key parameters on the soundness, microstructure and mechanical properties of the fabricated parts, sixty three combinations of laser power (twelve levels) and scanning speed (sixteen levels) with fifty eight levels of laser energy densities were realized in a single Inconel 718 alloy bar shaped specimen using the laser powder-bed fusion (L-PBF) technique. The combination of parameters varied from bottom to top of the bar, with each combination repeating every eight layers. Its spatial porosity distribution was measured by the Computed tomography (CT) test; its microstructure was observed by optical microscope, scanning electronic microscope and EBSD; the microhardness was measured as well. A comprehensive view of the relationship of these parameters and the porosity fraction, melt pool stacking, primary grain arm spacing and microhardness was obtained. Although high laser power and slow scanning speed are helpful to achieve low porosity, but the laser power has more significant effect on the quality of the specimen than the scanning speed. Only if at high levels the volumetric laser energy density could be used as an index to correlate to the quality of the specimen. The processing chart for the guidance of L-PBF was obtained. As the laser power is higher than 140 W and the scanning speed lower than 1000 mm/s, sound specimens would be realized. This method demonstrated the great potential for high throughput investigations of the L-PBF process.

A Lightweight Formalism for Reference Lifetimes and Borrowing in Rust

Rust is a relatively new programming language that has gained significant traction since its v1.0 release in 2015. Rust aims to be a systems language that competes with C/C++. A claimed advantage of Rust is a strong focus on memory safety without garbage collection. This is primarily achieved through two concepts, namely, reference lifetimes and borrowing . Both of these are well-known ideas stemming from the literature on region-based memory management and linearity / uniqueness . Rust brings both of these ideas together to form a coherent programming model. Furthermore, Rust has a strong focus on stack-allocated data and, like C/C++ but unlike Java, permits references to local variables. Type checking in Rust can be viewed as a two-phase process: First, a traditional type checker operates in a flow-insensitive fashion; second, a borrow checker enforces an ownership invariant using a flow-sensitive analysis. In this article, we present a lightweight formalism that captures these two phases using a flow-sensitive type system that enforces “ type and borrow safety .” In particular, programs that are type and borrow safe will not attempt to dereference dangling pointers. Our calculus core captures many aspects of Rust, including copy- and move-semantics, mutable borrowing, reborrowing, partial moves, and lifetimes. In particular, it remains sufficiently lightweight to be easily digested and understood and, we argue, still captures the salient aspects of reference lifetimes and borrowing. Furthermore, extensions to the core can easily add more complex features (e.g., control-flow, tuples, method invocation). We provide a soundness proof to verify our key claims of the calculus. We also provide a reference implementation in Java with which we have model checked our calculus using over 500B input programs. We have also fuzz tested the Rust compiler using our calculus against 2B programs and, to date, found one confirmed compiler bug and several other possible issues.

A Fuzzy Take on the Logical Issues of Statistical Hypothesis Testing

Statistical Hypothesis Testing (SHT) is a class of inference methods whereby one makes use of empirical data to test a hypothesis and often emit a judgment about whether to reject it or not. In this paper, we focus on the logical aspect of this strategy, which is largely independent of the adopted school of thought, at least within the various frequentist approaches. We identify SHT as taking the form of an unsound argument from Modus Tollens in classical logic, and, in order to rescue SHT from this difficulty, we propose that it can instead be grounded in t-norm based fuzzy logics. We reformulate the frequentists’ SHT logic by making use of a fuzzy extension of Modus Tollens to develop a model of truth valuation for its premises. Importantly, we show that it is possible to preserve the soundness of Modus Tollens by exploring the various conventions involved with constructing fuzzy negations and fuzzy implications (namely, the S and R conventions). We find that under the S convention, it is possible to conduct the Modus Tollens inference argument using Zadeh’s compositional extension and any possible t-norm. Under the R convention we find that this is not necessarily the case, but that by mixing R-implication with S-negation we can salvage the product t-norm, for example. In conclusion, we have shown that fuzzy logic is a legitimate framework to discuss and address the difficulties plaguing frequentist interpretations of SHT.

Model checking agent-based communities against uncertain group commitments and knowledge

In recent years, the use of Multi-Agent Systems (MASs) to solve complex problems has grown rapidly. Social communicative commitments have been widely employed in such systems as a means of communication allowing heterogeneous agents to cooperate. However, to prevent undesirable outcomes, communicative commitments and their interactions with agents’ knowledge need to be verified. This paper aims at verifying MASs where agents have knowledge and communicate through manipulating uncertain social commitments, especially when the scope of commitments moves beyond the common agent-to-agent scheme. We introduce a model checking method for verifying those systems and capitalize on the interaction between not only individual but also group communicative commitments and knowledge in the presence of uncertainty. System’s properties are expressed using the Probabilistic Computation Tree Logic of Knowledge and Commitment (PCTLkc+). In the proposed approach, model checking PCTLkc+ is reduced to model checking the probabilistic branching-time logic PCTL. This is achieved by transforming PCTLkc+ model to a Markov Decision Process (MDP), and reducing PCTLkc+ formulae into PCTL formulae compatible with PRISM, a reference model checking tool for probabilistic temporal systems. Thereafter, we provide the soundness and completeness proofs of the reduction technique, and compute its time complexity. The effectiveness of the proposed approach is evaluated by implementing it on top of PRISM using two concrete applications, namely Online Shopping System from the business domain, and Insurance Claim Processing from the industrial domain. The obtained results of the two case studies underscore the scientific value of our proposed framework and confirm that verifying commitment-based probabilistic epistemic MASs has become attainable by utilizing this approach. The presented work outperforms existing proposals because it considers the problem of modeling and verifying MASs where group social commitments are interacting with participating agents’ knowledge in the presence of uncertainty, which has not been addressed yet in the literature.

THE LOGIC OF THE EVIDENTIAL CONDITIONAL

AbstractIn some recent works, Crupi and Iacona proposed an analysis of ‘if’ based on Chrysippus’ idea that a conditional holds whenever the negation of its consequent is incompatible with its antecedent. This paper presents a sound and complete system of conditional logic that accommodates their analysis. The soundness and completeness proofs that will be provided rely on a general method elaborated by Raidl, which applies to a wide range of systems of conditional logic.

On checking equivalence of simulation scripts

To support Model Based Design of Cyber-Physical Systems (CPSs) many simulation based approaches to System Level Formal Verification (SLFV) have been devised. Basically, these are Bounded Model Checking approaches (since simulation horizon is of course bounded) relying on simulators to compute the system dynamics and thereby verify the given system properties. The main obstacle to simulation based SLFV is the large number of simulation scenarios to be considered and thus the huge amount of simulation time needed to complete the verification task. To save on computation time, simulation based SLFV approaches exploit the capability of simulators to save and restore simulation states. Essentially, such a time saving is obtained by optimising the simulation script defining the simulation activity needed to carry out the verification task. Although such approaches aim to (bounded) formal verification, as a matter of fact, the proof of correctness of the methods to optimise simulation scripts basically relies on an intuitive semantics for simulation scripting languages. This hampers the possibility of formally showing that the optimisations introduced to speed up the simulation activity do not actually omit checking of relevant behaviours for the system under verification. The aim of this paper is to fill the above gap by presenting an operational semantics for simulation scripting languages and by proving soundness and completeness properties for it. This, in turn, enables formal proofs of equivalence between unoptimised and optimised simulation scripts.

EVALUATION OF MINE WASTE ROCKS FOR USE AS MATERIALS FOR ROAD CONSTRUCTION

Mine rock wastes are materials that are removed in order to access and mine the ore. They pose significant environmental challenges due to their existence in large volumes. The chemical and geomechanical properties of mine rock wastes were determined to aid in assessing their suitability for use as aggregates for road construction. The chemical and geotechnical test performed on the samples were Sulphate, pH, Aggregate Crushing Value, Sodium Sulphate Soundness, Aggregate Impact Value, Specific Gravity, Bulk Density, Water Absorption, Los Angeles Abrasion Value, and XRF analysis, which was conducted in accordance with the British Standard (BS) and American Society for Testing and Materials (ASTM) Standards.The test results obtained indicated that, all the samples passed the British Standard (BS) and American Society for Testing and Materials ( ASTM ) making them suitable to be used as aggregates for road construction. The results obtained further showed that the Banket Sandstone is the best material to be used as aggregates substitute for road construction among all the waste rocks in Damang since it was relatively the most optimum rock type.

A graded dependent type system with a usage-aware semantics

Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop GraD, a novel version of such a graded dependent type system that includes functions, tensor products, additive sums, and a unit type. Since standard operational semantics is resource-agnostic, we develop a heap-based operational semantics and prove a soundness theorem that shows correct accounting of resource usage. Several useful properties, including the standard type soundness theorem, non-interference of irrelevant resources in computation and single pointer property for linear resources, can be derived from this theorem. We hope that our work will provide a base for integrating linearity, irrelevance and dependent types in practical programming languages like Haskell.

Modeling and analyzing evaluation cost of CUDA kernels

General-purpose programming on GPUs (GPGPU) is becoming increasingly in vogue as applications such as machine learning and scientific computing demand high throughput in vector-parallel applications. NVIDIA's CUDA toolkit seeks to make GPGPU programming accessible by allowing programmers to write GPU functions, called kernels, in a small extension of C/C++. However, due to CUDA's complex execution model, the performance characteristics of CUDA kernels are difficult to predict, especially for novice programmers. This paper introduces a novel quantitative program logic for CUDA kernels, which allows programmers to reason about both functional correctness and resource usage of CUDA kernels, paying particular attention to a set of common but CUDA-specific performance bottlenecks. The logic is proved sound with respect to a novel operational cost semantics for CUDA kernels. The semantics, logic and soundness proofs are formalized in Coq. An inference algorithm based on LP solving automatically synthesizes symbolic resource bounds by generating derivations in the logic. This algorithm is the basis of RaCuda, an end-to-end resource-analysis tool for kernels, which has been implemented using an existing resource-analysis tool for imperative programs. An experimental evaluation on a suite of CUDA benchmarks shows that the analysis is effective in aiding the detection of performance bugs in CUDA kernels.

Formal Approach Based on Petri Nets for Modeling and Verification of Video Games

Video games are complex systems that combine technical and artistic processes. The specification of this type of system is not a trivial task, making it necessary to use diagrams and charts to visually specify sets of requirements. Therefore, the underlying proposal of this work is to present an approach based on the formalism of Petri nets for aiding in the design process of video games. The activities of the game are represented by a specific type of Petri net called WorkFlow net. The definition of a topological map can be represented by state graphs. Using Colored Petri nets, it is possible to define formal communication mechanisms between the model of activity and the model of the map. The simulation of the timed models allows then to produce an estimated time that corresponds to the effective duration a player will need to complete a level of a game. Furthermore, a kind of Soundness property related to gameplay in a game Quest can be verified through state space analysis. For a better understanding of the approach, the video game Silent Hill II is used.

Dischargeable Obligations in the 𝒮CIFF Framework

Abductive Logic Programming (ALP) has been proven very effective for formalizing societies of agents, commitments and norms, in particular by mapping the most common deontic operators (obligation, prohibition, permission) to abductive expectations. In our previous works, we have shown that ALP is a suitable framework for representing norms. Normative reasoning and query answering were accommodated by the same abductive proof procedure, named 𝒮CIFF. In this work, we introduce a defeasible flavour in this framework, in order to possibly discharge obligations in some scenarios. Abductive expectations can also be qualified as dischargeable, in the new, extended syntax. Both declarative and operational semantics are improved accordingly, and proof of soundness is given under syntax allowedness conditions Moreover, the dischargement itself might be proved invalid, or incoherent with the rules, due to new knowledge provided later on. In such a case, a discharged expectation might be reinstated and hold again after some evidence is given. We extend the notion of dischargement to take into consideration also the reinstatement of expectations. The expressiveness and power of the extended framework, named 𝒮CIFF𝒟, is shown by modeling and reasoning upon a fragment of the Japanese Civil Code. In particular, we consider a case study concerning manifestations of intention and their rescission (Section II of the Japanese Civil Code).

The Athenian against Atheists: Theological Persuasion in Plato’s Laws

This paper examines the argument for the existence of gods, formulated by the Athenian in the 10th book of Plato’s Laws. The purpose of this investigation is to find out whether the argument persuades its intended audience – the atheists. The analysis is divided into three parts: 1) the investigation of the Athenian’s concept of persuasion; 2) the examination of the argument’s audience; 3) the reconstruction of the argument and the evaluation of its logical soundness, compliance with the defined criteria of persuasion, and suitability for the defined audience. This paper argues that the Athenian’s argument for the existence of gods should persuade atheists.

Sí hay negación lógica

En este artículo discutimos la tesis de Jc Beall según la cual no hay negación lógica. Evaluamos la solidez del argumento con el que defiende su tesis y presentamos dos razones para rechazar una de sus premisas: que la negación tiene que ser excluyente o exhaustiva. La primera razón involucra una presentación alternativa de las reglas de la negación en sistemas de secuentes diferentes al que Beall presupone. La segunda razón establece que la negación no tiene que ser excluyente o exhaustiva.

A clock-based dynamic logic for the verification of CCSL specifications in synchronous systems

The Clock Constraint Specification Language (CCSL) is a clock-based specification language for real-time embedded systems. With logical clocks defined as first-class citizens, CCSL provides a natural way for describing clock constraints in synchronous systems — a classical model of concurrency for real-time embedded systems. In this paper, we propose a clock-based dynamic logic called CCSL Dynamic Logic (CDL) for the verification of CCSL specifications in synchronous systems. It extends the first-order dynamic logic with a synchronous execution mechanism in its program model and with CCSL primitives as terms in its logical formulae. We build a sound and relatively complete proof system for CDL to support the verification. Compared with previous approaches for verifying CCSL specifications, which are based on model checking and SMT checking techniques, our approach, which is based on theorem-proving, offers a unified verification framework in which both bounded and unbounded CCSL specifications can be verified. Technically, with the proof system of CDL, a complex CDL formula can be semi-automatically transformed into a set of quantifier-free, arithmetical first-order logic (QF-AFOL) formulae which can be checked by an SMT solver in an efficient way. As a case study, we analyze a simple synchronous system throughout the paper to illustrate how CDL works. We analyze and prove the soundness and completeness of the proof system for CDL. Currently, CDL is partially mechanized in Coq. • Dynamic Logic to deal with Logical Clocked Systems. • Proof system for CCSL and synchronous systems. • Rely on a decidable subset theory for efficient use of SMT solvers. • Proof of soundness and relative completeness.