Paracomplete logic Kl: natural deduction, its automation, complexity and applications

In the development of many modern software solutions where the underlying systems are complex, dynamic and heterogeneous, the significance of specification-based verification is well accepted. However, often parts of the specification may not be known. Yet reasoning based on such incomplete specifications is very desirable. Here, paracomplete logics seem to be an appropriate formal setup: opposite to Tarski’s theory of truth with its principle of bivalence, in these logics a statement and its negation may be both untrue. An immediate result is that the law of excluded middle becomes invalid. In this paper we show a way to apply an automatic proof searching procedure for the paracomplete logic Kl to reason about incomplete information systems. We provide an original account of complexity of natural deduction systems, leading us closer to the efficiency of the presented proof search algorithm. Moreover, we have turned the assumptions management into an advantage showing the applicability of the proposed technique to assume-guarantee reasoning

Lifted Variable Elimination for Probabilistic Logic Programming

Lifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances. Even if various authors have underlined its importance for probabilistic logic programming (PLP), lifted inference has been applied up to now only to relational languages outside of logic programming. In this paper we adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the problem of computing the probability of queries to probabilistic logic programs under the distribution semantics. In particular, we extend the Prolog Factor Language (PFL) to include two new types of factors that are needed for representing ProbLog programs. These factors take into account the existing causal independence relationships among random variables and are managed by the extension to variable elimination proposed by Zhang and Poole for dealing with convergent variables and heterogeneous factors. Two new operators are added to GC-FOVE for treating heterogeneous factors. The resulting algorithm, called LP$^2$ for Lifted Probabilistic Logic Programming, has been implemented by modifying the PFL implementation of GC-FOVE and tested on three benchmarks for lifted inference. A comparison with PITA and ProbLog2 shows the potential of the approach.Comment: To appear in Theory and Practice of Logic Programming (TPLP). arXiv admin note: text overlap with arXiv:1402.0565 by other author

Bounded Rationality and Heuristics in Humans and in Artificial Cognitive Systems

In this paper I will present an analysis of the impact that the notion of “bounded rationality”, introduced by Herbert Simon in his book “Administrative Behavior”, produced in the field of Artificial Intelligence (AI). In particular, by focusing on the field of Automated Decision Making (ADM), I will show how the introduction of the cognitive dimension into the study of choice of a rational (natural) agent, indirectly determined - in the AI field - the development of a line of research aiming at the realisation of artificial systems whose decisions are based on the adoption of powerful shortcut strategies (known as heuristics) based on “satisficing” - i.e. non optimal - solutions to problem solving. I will show how the “heuristic approach” to problem solving allowed, in AI, to face problems of combinatorial complexity in real-life situations and still represents an important strategy for the design and implementation of intelligent systems

On the cost-complexity of multi-context systems

Multi-context systems provide a powerful framework for modelling information-aggregation systems featuring heterogeneous reasoning components. Their execution can, however, incur non-negligible cost. Here, we focus on cost-complexity of such systems. To that end, we introduce cost-aware multi-context systems, an extension of non-monotonic multi-context systems framework taking into account costs incurred by execution of semantic operators of the individual contexts. We formulate the notion of cost-complexity for consistency and reasoning problems in MCSs. Subsequently, we provide a series of results related to gradually more and more constrained classes of MCSs and finally introduce an incremental cost-reducing algorithm solving the reasoning problem for definite MCSs