1,777 research outputs found
Reasoning about Knowledge and Belief: A Syntactical Treatment
The study of formal theories of agents has intensified over the last couple of decades, since such formalisms can be viewed as providing the specifications for building rational agents and multi-agent systems. Most of the proposed approaches are based upon the well-understood framework of modal logics and possible world semantics. Although intuitive and expressive, these approaches lack two properties that can be considered important to a rational agent's reasoning: quantification over the propositional attitudes, and self-referential statements. This paper presents an alternative framework which is different from those found in the literature in two ways: Firstly, a syntactical approach for the representation of the propositional attitudes is adopted. This involves the use of a truth predicate and syntactic modalities which are defined in terms of the truth predicate itself and corresponding modal operators. Secondly, an agent's information state includes both knowledge and beliefs. Independent modal operators for the two notions are introduced and based on them syntactic modalities are defined. Furthermore, the relation between knowledge and belief is thoroughly explored and three different connection axiomatisations for the modalities and the syntactic modalities are proposed and their properties investigated
Strategy Logic with Imperfect Information
We introduce an extension of Strategy Logic for the imperfect-information
setting, called SLii, and study its model-checking problem. As this logic
naturally captures multi-player games with imperfect information, the problem
turns out to be undecidable. We introduce a syntactical class of "hierarchical
instances" for which, intuitively, as one goes down the syntactic tree of the
formula, strategy quantifications are concerned with finer observations of the
model. We prove that model-checking SLii restricted to hierarchical instances
is decidable. This result, because it allows for complex patterns of
existential and universal quantification on strategies, greatly generalises
previous ones, such as decidability of multi-player games with imperfect
information and hierarchical observations, and decidability of distributed
synthesis for hierarchical systems. To establish the decidability result, we
introduce and study QCTL*ii, an extension of QCTL* (itself an extension of CTL*
with second-order quantification over atomic propositions) by parameterising
its quantifiers with observations. The simple syntax of QCTL* ii allows us to
provide a conceptually neat reduction of SLii to QCTL*ii that separates
concerns, allowing one to forget about strategies and players and focus solely
on second-order quantification. While the model-checking problem of QCTL*ii is,
in general, undecidable, we identify a syntactic fragment of hierarchical
formulas and prove, using an automata-theoretic approach, that it is decidable.
The decidability result for SLii follows since the reduction maps hierarchical
instances of SLii to hierarchical formulas of QCTL*ii
Ten virtues of structured graphs
This paper extends the invited talk by the first author about the virtues
of structured graphs. The motivation behind the talk and this paper relies on our
experience on the development of ADR, a formal approach for the design of styleconformant,
reconfigurable software systems. ADR is based on hierarchical graphs
with interfaces and it has been conceived in the attempt of reconciling software architectures
and process calculi by means of graphical methods. We have tried to
write an ADR agnostic paper where we raise some drawbacks of flat, unstructured
graphs for the design and analysis of software systems and we argue that hierarchical,
structured graphs can alleviate such drawbacks
Nonlinear Models of Neural and Genetic Network Dynamics:\ud \ud Natural Transformations of Ĺukasiewicz Logic LM-Algebras in a Ĺukasiewicz-Topos as Representations of Neural Network Development and Neoplastic Transformations \ud
A categorical and Ĺukasiewicz-Topos framework for Algebraic Logic models of nonlinear dynamics in complex functional systems such as Neural Networks, Cell Genome and Interactome Networks is introduced. Ĺukasiewicz Algebraic Logic models of both neural and genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable next-state/transfer functions is extended to a Ĺukasiewicz Topos with an N-valued Ĺukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis.\u
Ĺukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models
A categorical and Ĺukasiewicz-Topos framework for Algebraic Logic models of nonlinear dynamics in complex functional systems such as Neural Networks, Cell Genome and Interactome Networks is introduced. Ĺukasiewicz Algebraic Logic models of both neural and genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Ĺukasiewicz Topos with an n-valued Ĺukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis
Inconsistency, paraconsistency and Ď-inconsistency
In this paper I'll explore the relation between Ď-inconsistency and plain inconsistency, in the context of theories that intend to capture semantic concepts. In particular, I'll focus on two very well known inconsistent but non-trivial theories of truth: LP and STTT. Both have the interesting feature of being able to handle semantic and arithmetic concepts, maintaining the standard model. However, it can be easily shown that both theories are Ď-inconsistent. Although usually a theory of truth is generally expected to be Ď-consistent, all conceptual concerns don't apply to inconsistent theories. Finally, I'll explore if it's possible to have an inconsistent, but Ď-consistent theory of truth, restricting my analysis to substructural theories.Fil: Da Re, Bruno. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂŠcnicas; Argentina. Instituto de Investigaciones FilosĂłficas - Sadaf; Argentin
Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models
Operational logic and bioinformatics models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes are proposed. Łukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Łukasiewicz Topos with an n-valued Łukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis
A first-order epistemic quantum computational semantics with relativistic-like epistemic effects
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. In these logics well-formed formulas are supposed to denote pieces of quantum information: possible pure states of quantum systems that can store the information in question. At the same time, the logical connectives are interpreted as quantum logical gates: unitary operators that process quantum information in a reversible way, giving rise to quantum circuits. Quantum computational logics have been mainly studied as sentential logics (whose alphabet consists of atomic sentences and of logical connectives). In this article we propose a semantic characterization for a first-order epistemic quantum computational logic, whose language can express sentences like "Alice knows that everybody knows that she is pretty". One can prove that (unlike the case of logical connectives) both quantifiers and epistemic operators cannot be generally represented as (reversible) quantum logical gates. The "act of knowing" and the use of universal (or existential) assertions seem to involve some irreversible "theoretic jumps", which are similar to quantum measurements. Since all epistemic agents are characterized by specific epistemic domains (which contain all pieces of information accessible to them), the unrealistic phenomenon of logical omniscience is here avoided: knowing a given sentence does not imply knowing all its logical consequences
Internal Calculi for Separation Logics
We present a general approach to axiomatise separation logics with heaplet semantics with no external features such as nominals/labels. To start with, we design the first (internal) Hilbert-style axiomatisation for the quantifier-free separation logic SL(?, -*). We instantiate the method by introducing a new separation logic with essential features: it is equipped with the separating conjunction, the predicate ls, and a natural guarded form of first-order quantification. We apply our approach for its axiomatisation. As a by-product of our method, we also establish the exact expressive power of this new logic and we show PSpace-completeness of its satisfiability problem
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