Nonvolatile stateful logic through RRAM is a promising route to build in-memory computing architecture. In this letter, a logic methodology based on 1T1R structure has been proposed to implement ...functionally complete Boolean logics. Arbitrary logic functions could be realized in two steps: initialization and writing. An additional read step is required to read out the logic result, which is in situ stored in the nonvolatile resistive state of the memory. Cascade problem in building larger logic circuits is also discussed. Our 1T1R logic device and operation method could be beneficial for massive integration and practical application of RRAM-based logic.
Qualitative reasoning in a two-layered framework Bílková, Marta; Frittella, Sabine; Kozhemiachenko, Daniil ...
International journal of approximate reasoning,
March 2023, 2023-03-00, 2023-03, Letnik:
154
Journal Article
Recenzirano
Odprti dostop
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events.
...The paper is divided into two parts. In the first part, we formalise reasoning with the qualitative counterparts of capacities, belief functions, and probabilities, within the framework of two-layered logics. Namely, we provide two-layered logics built over the classical propositional logic using a unary belief modality B that connects the inner layer to the outer one where the reasoning is formalised by means of Gödel logic. We design their Hilbert-style axiomatisations and prove their completeness. In the second part, we discuss the paraconsistent generalisations of the logics for qualitative uncertainty that take into account the case of the available information being contradictory or inconclusive.
We design an expansion of Belnap–Dunn logic with belief and plausibility functions that allows non-trivial reasoning with contradictory and incomplete probabilistic information. We also formalise ...reasoning with non-standard probabilities and belief functions in two ways. First, using a calculus of linear inequalities, akin to the one presented in 23. Second, as a two-layered modal logic wherein reasoning with evidence (the outer layer) utilises paraconsistent expansions of Łukasiewicz logic. The second approach is inspired by 3. We prove completeness for both kinds of calculi and show their equivalence by establishing faithful translations in both directions.
This paper considers the callback reachability problem --- determining if a callback can be called by an event-driven framework in an unexpected state. Event-driven programming frameworks are ...pervasive for creating user-interactive applications (apps) on just about every modern platform. Control flow between callbacks is determined by the framework and largely opaque to the programmer. This opacity of the callback control flow not only causes difficulty for the programmer but is also difficult for those developing static analysis. Previous static analysis techniques address this opacity either by assuming an arbitrary framework implementation or attempting to eagerly specify all possible callback control flow, but this is either too coarse to prove properties requiring callback-ordering constraints or too burdensome and tricky to get right. Instead, we present a middle way where the callback control flow can be gradually refined in a targeted manner to prove assertions of interest. The key insight to get this middle way is by reasoning about the history of method invocations at the boundary between app and framework code --- enabling a decoupling of the specification of callback control flow from the analysis of app code. We call the sequence of such boundary-method invocations message histories and develop message-history logics to do this reasoning. In particular, we define the notion of an application-only transition system with boundary transitions, a message-history program logic for programs with such transitions, and a temporal specification logic for capturing callback control flow in a targeted and compositional manner. Then to utilize the logics in a goal-directed verifier, we define a way to combine after-the-fact an assertion about message histories with a specification of callback control flow. We implemented a prototype message history-based verifier called Historia and provide evidence that our approach is uniquely capable of distinguishing between buggy and fixed versions on challenging examples drawn from real-world issues and that our targeted specification approach enables proving the absence of multi-callback bug patterns in real-world open-source Android apps.
We study probabilistic-logic reasoning in a context that allows for “partial truths”, focusing on computational and algorithmic properties of non-classical Łukasiewicz Infinitely-valued Probabilistic ...Logic. In particular, we study the satisfiability of joint probabilistic assignments, which we call ŁIPSAT. Although the search space is initially infinite, we provide linear algebraic methods that guarantee polynomial size witnesses, placing ŁIPSAT complexity in the NP-complete class. An exact satisfiability decision algorithm is presented which employs, as a subroutine, the decision problem for Łukasiewicz Infinitely-valued (non probabilistic) logic, that is also an NP-complete problem. We investigate efficient representation of rational McNaughton functions in Łukasiewicz Infinitely-valued Logic modulo satisfiability.
This paper presents a generalization of Fine’s completeness theorem for transitive logics of finite width, and proves the Kripke completeness of transitive logics of finite “suc-eq-width”. The frame ...condition for each finite suc-eq-width axiom requires, in rooted transitive frames, a finite upper bound of cardinality for antichains of points with different proper successors. The paper also presents a generalization of Rybakov’s completeness theorem for transitive logics of prefinite width, and proves the Kripke completeness of transitive logics of prefinite “suc-eq-width”. The frame condition for each prefinite suc-eq-width axiom requires, in rooted transitive frames, a finite upper bound of cardinality for antichains of points that have a finite lower bound of depth and have different proper successors. We will construct continuums of transitive logics of finite suc-eq-width but not of finite width, and continuums of those of prefinite suc-eq-width but not of prefinite width. This shows that our new completeness results cover uncountably many more logics than Fine’s theorem and Rybakov’s theorem respectively.
The business model has been conceived as a commercial logic of value proposition, creation, exchange and capture. However, its underlying conceptual structure of an organizational value logic holds ...promise also for application beyond a purely commercial context, for partially commercial and even noncommercial organizations. This paper unlocks this potential by conceptualizing homogeneous and heterogeneous organizational value logics shaped by a variety of institutional logics. Homogeneous value logics are dominantly shaped by individual institutional logics, such as the value logic of businesses shaped by an institutional logic of the commercial market, or that of a churches shaped by an institutional logic of religion. Heterogeneous value logics, however, are co-shaped by two or more institutional logics. The application of these concepts is exemplified in the context of sustainability business models, which are built on a heterogeneous value logic that combines elements from commercial, sustainability, welfare and government logics. The paper contributes to the business model discussion by extending it to partially commercial and noncommercial organizations; by creating a conceptual space between value logics and institutional logics; and by proposing the meta-logic of value proposition, creation, exchange and capture, a novel analytical tool for the study of organizations shaped by plural institutional logics.
Display omitted
Generalized Revenge Murzi, Julien; Rossi, Lorenzo
Australasian journal of philosophy,
01/2020, Letnik:
98, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Since Saul Kripke's influential work in the 1970s, the revisionary approach to semantic paradox-the idea that semantic paradoxes must be solved by weakening classical logic-has been increasingly ...popular. In this paper, we present a new revenge argument to the effect that the main revisionary approaches breed new paradoxes that they are unable to block.
This paper presents an abstract study of completeness properties of non-classical logics with respect to matricial semantics. Given a class of reduced matrix models we define three completeness ...properties of increasing strength and characterize them in several useful ways. Some of these characterizations hold in absolute generality and others are for logics with generalized implication or disjunction connectives, as considered in the previous papers. Finally, we consider completeness with respect to matrices with a linear dense order and characterize it in terms of an extension property and a syntactical metarule. This is the final part of the investigation started and developed in the papers (Cintula and Noguera in Arch Math Logic 49(4):417–446,
2010
; Arch Math Logic 53(3):353–372,
2016
).
Attempts at combining logic and neural networks into neurosymbolic approaches have been on the increase in recent years. In a neurosymbolic system, symbolic knowledge assists deep learning, which ...typically uses a sub-symbolic distributed representation, to learn and reason at a higher level of abstraction. We present Logic Tensor Networks (LTN), a neurosymbolic framework that supports querying, learning and reasoning with both rich data and abstract knowledge about the world. LTN introduces a fully differentiable logical language, called Real Logic, whereby the elements of a first-order logic signature are grounded onto data using neural computational graphs and first-order fuzzy logic semantics. We show that LTN provides a uniform language to represent and compute efficiently many of the most important AI tasks such as multi-label classification, relational learning, data clustering, semi-supervised learning, regression, embedding learning and query answering. We implement and illustrate each of the above tasks with several simple explanatory examples using TensorFlow 2. The results indicate that LTN can be a general and powerful framework for neurosymbolic AI.
PDF
