Logics of Involutive Stone Algebras

An involutive Stone algebra (IS-algebra) is a structure that is simultaneously a De Morgan algebra and a Stone algebra (i.e. a pseudo-complemented distributive lattice satisfying the well-known Stone identity, ∼ x ∨ ∼ ∼ x ≈ 1). IS-algebras have been studied algebraically and topologically since the 1980’s, but a corresponding logic (here denoted IS ≤ ) has been introduced only very recently. The logic IS ≤ is the departing point for the present study, which we then extend to a wide family of previously unknown logics defined from IS-algebras. We show that IS ≤ is a conservative expansion of the Belnap-Dunn four-valued logic (i.e. the order-preserving logic of the variety of De Morgan algebras), and we give a finite Hilbert-style axiomatization for it. More generally, we introduce a method for expanding conservatively every super-Belnap logic so as to obtain an extension of IS ≤ . We show that every logic thus defined can be axiomatized by adding a fixed finite set of rule schemata to the corresponding super-Belnap base logic. We also consider a few sample extensions of IS ≤ that cannot be obtained in the above- described way, but can nevertheless be axiomatized finitely by other methods. Most of our axiomatization results are obtained in two steps: through a multiple-conclusion calculus first, which we then reduce to a traditional one. The multiple-conclusion axiomatizations introduced in this process, being analytic, are of independent interest from a proof-theoretic standpoint. Our results entail that the lattice of super-Belnap logics (which is known to be uncountable) embeds into the lattice of extensions of IS ≤ . Indeed, as in the super-Belnap case, we establish that the finitary extensions of IS ≤ are already uncountably many.

Serial verb constructions and covert coordinations in Edo – an analysis in Type Logical Grammar

Based on both syntactic and semantic criteria, Stewart (2001) and, following him, Baker and Stewart (1999), distinguish two types of serial verb constructions (SVC) and one type of covert coordination (CC) in Edo. In this article, we present an analysis of these constructions, using Type Logical Grammar (TLG) with an event-based semantic component. We choose as base logic the non-associative Lambek calculus augmented with two unary multiplicative connectives (NL(◊, □)). SVCs and CCs are interpreted as complex event structures. The complex predicates underlying these structures are derived from simple verbs by means of a constructor. SVCs and CCs differ in terms of which part of the complex event structure is denoted. For SVCs, this is the sum of all events in the structure whereas for a CC this is only the first event in the sequence. The two verbs in an SVC and a CC are treated asymmetrically by assuming that the first verb has an extended subcategorization frame. The additional argument is of type vp (possibly modally decorated). Constraints on word order and the realization of arguments are accounted for using structural rules like permutation and contraction. The application of these rules is enforced by making use of the unary connectives.

A logic of knowledge based on abstract arguments

We introduce a logic of knowledge in a framework in which knowledge is treated as a kind of belief. The framework is based on a standard KD45 characterization of belief, and the characterization of knowledge undergoes the classical tripartite analysis that knowledge is justified true belief, which has a natural link to the studies of logics of evidence and justification. The interpretation of knowledge avoids the unwanted properties of logical omniscience, independent of the choice of the base logic of belief. We axiomatize the logic, prove its soundness and completeness and study the computational complexity results of the model checking and satisfiability problems. We extend the logic to a multi-agent setting and introduce a variant in which belief is characterized in a weaker system to avoid the problem of logical omniscience.

Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic

Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which are characterised by the feature that the inference process may require to retract prior conclusions given additional premisses. This nonmonotonic aspect is in contrast to valid inference relations, which are monotonic. Although nonmonotonic reasoning has been extensively studied in the literature, only few works exist dealing with a proper proof theory for specific logics. In this paper, we introduce sequent-type calculi for two variants of default logic, viz., on the one hand, for three-valued default logic due to Radzikowska, and on the other hand, for disjunctive default logic, due to Gelfond, Lifschitz, Przymusinska, and Truszczyński. The first variant of default logic employs Łukasiewicz’s three-valued logic as the underlying base logic and the second variant generalises defaults by allowing a selection of consequents in defaults. Both versions have been introduced to address certain representational shortcomings of standard default logic. The calculi we introduce axiomatise brave reasoning for these versions of default logic, which is the task of determining whether a given formula is contained in some extension of a given default theory. Our approach follows the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti, which employs a rejection calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults.

Design of Indoor Room Gas CO and SO2 Detection Based on Microcontroller Using Fuzzy Logic

The incidence of poisoning due to carbon monoxide gas arising from drilling activities on the first floor of a building in the Kelapa Gading beauty clinic in Jakarta resulted in 17 people experiencing poisoning. In this study developing a device on the sensor used to detect CO and SO2 gas, in the air of a closed room using gas sensor MQ 135 and MQ 136. The results of testing the CO and SO2 gas gauges using samples of cigarette smoke and sulfur powder using MQ 135 and MQ 136 sensors with fuzzy rule base logic for motor speed to produce CO and SO2 gas, that obtained a value of 0.233 ppm SO2 gas safe conditions and gas input CO with the sensor obtained a value of 0.513 ppm, the condition is safe so that the output is 49.8 ppm, the condition of the fan blower does not rotate. Whereas when the reading value of 5.0 ppm is very concentrated and the CO gas input with the sensor is 13.8 ppm the condition is very concentrated producing an output of 228 ppm the very danger.

A Logic for Verifying Metric Temporal Properties in Distributed Hybrid Systems

We introduce a logic for specifying and verifying metric temporal properties of distributed hybrid systems that combines quantified differential dynamic logic (QdL) for reasoning about the possible behavior of distributed hybrid systems with metric temporal logic (MTL) for reasoning about the metric temporal behavior during their operation. For our combined logic, we generalize the semantics of dynamic modalities to refer to hybrid traces instead of final states. Further, we prove that this gives a conservative extension of QdL for distributed hybrid systems. On this basis, we provide a modular verification calculus that reduces correctness of metric temporal behavior of distributed hybrid systems to generic temporal reasoning and then non-temporal reasoning, and prove that we obtain a complete axiomatization relative to the non-temporal base logic QdL.

A comprehensible guide to a new unifier for CIC including universe polymorphism and overloading

Unification is a core component of every proof assistant or programming language featuring dependent types. In many cases, it must deal with higher order problems up to conversion. Since unification in such conditions is undecidable, unification algorithms may include several heuristics to solve common problems. However, when the stack of heuristics grows large, the result and complexity of the algorithm can become unpredictable. Our contributions are twofold: (1) We present a full description of a new unification algorithm for the Calculus of Inductive Constructions (the base logic of COQ), building it up from a basic calculus to the full Calculus of Inductive Constructions as it is implemented in COQ, including universe polymorphism, canonical structures (the overloading mechanism baked into COQ's unification), and a small set of useful heuristics. (2) We implemented our algorithm, and tested it on several libraries, providing evidence that the selected set of heuristics suffices for large developments.

Finite Element Analysis and Measurement of Low-Profile BVATMPackage On Package (PoP) Warpage Characteristics

Mobile electronics developers continue to demand lower-profile components in order to achieve thinner, higher-performing handheld products. This requirement extends to the commonly used Package-on-Package (PoP) configuration where recent trends are demanding 1.0mm or less total height for the stacked processor and memory components. Bond-Via-Array (BVTM technology facilitates next-generation Package-on-Package (PoP) by utilizing wirebond technology to achieve fine-pitch interconnects at controlled height. As with conventional PoP, thinner components present challenges to controlling the resulting package warpage. It is important to understand the warpage behavior of both the base Logic and topside memory packages in order to ensure a high-yielding stacking process. Limiting warpage to below 100um is critical for manufacturing as well as meeting thermo-mechanical reliability standards. Design and material selection for both components influence the warpage profiles. Utilizing Finite Element Analysis (FEA) we examine the influence of the overall structure and key material selection on package warpage in order to determine configurations for further reducing BVA PoP stack height. Analysis is based on a 1020 IO 14mm×14mm outline package test vehicle. A detailed analysis of results includes comparison of simulation data with measurements of actual samples with various materials and thicknesses. The FEA model is validated with prototype packages by measuring actual warpage as a function of temperature. Experimental data for exposed die and over-molded die samples are included in the completed results and analysis.

Semantics of templates in a compositional framework for building logics

There is a growing need for abstractions in logic specification languages such as FO(·) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always described through a syntactical rewriting scheme, we present an alternative view on templates as second order definitions. To extend the existing definition construct of FO(·) to second order, we introduce a powerful compositional framework for defining logics by modular integration of logic constructs specified as pairs of one syntactical and one semantical inductive rule. We use the framework to build a logic of nested second order definitions suitable to express templates. We show that under suitable restrictions, the view of templates as macros is semantically correct and that adding them does not extend the descriptive complexity of the base logic, which is in line with results of existing approaches.

Mtac: A monad for typed tactic programming in Coq

Effective support for custom proof automation is essential for large-scale interactive proof development. However, existing languages for automation via tactics either (a) provide no way to specify the behavior of tactics within the base logic of the accompanying theorem prover, or (b) rely on advanced type-theoretic machinery that is not easily integrated into established theorem provers.We present Mtac, a lightweight but powerful extension to Coq that supports dependently typed tactic programming. Mtac tactics have access to all the features of ordinary Coq programming, as well as a new set of typed tactical primitives. We avoid the need to touch the trusted kernel typechecker of Coq by encapsulating uses of these new tactical primitives in a monad, and instrumenting Coq so that it executes monadic tactics during type inference.