In this paper, we present a program designed to successfully and autonomously play Angry Birds which attempts to embrace motives of human players in their choices of targets they want to shoot at in a game play. The program comprises two modules: the representation module and the reasoning module. In the former we introduce qualitative space representation that utilises notions such as "to lie on", "to lie to the right", "to be a shelter of a target", etc. The latter investigates how particular blocks of a structure behave once one of them has been hit. It includes two algorithms, namely Vertical Impact and Horizontal Impact. The first one is a novel method of investigating the behaviour of complex structures after one of their constituent blocks gets hit. Namely, it predicts which elements of a structure fall if a supporting block gets destroyed. Horizontal Impact, on the other hand, simulates force propagation between adjacent elements after one of them gets struck. We also describe experimental tests we have conducted in which Vertical Impact correctly predicted which blocks will fall in over 98% of investigated cases.
DatalogMTL is an extension of Datalog with metric temporal operators that has recently received significant attention. In contrast to plain Datalog, where scalable implementations are often based on materialisation (a.k.a. forward chaining), reasoning algorithms for recursive fragments of DatalogMTL are automata-based and not well suited for practice. In this paper we propose the class of finitely materialisable DatalogMTL programs, for which forward chaining reasoning terminates after finitely many rounds of rule application. We show that, for bounded programs (a large fragment of DatalogMTL where temporal intervals are restricted to not mention infinity), checking whether a program is finitely materialisable is feasible in exponential time, and propose sufficient conditions for finite materialisability that can be checked more efficiently. We finally show that fact entailment over finitely materialisable bounded programs is ExpTime-complete, and hence no harder than Datalog reasoning.
Definite descriptions are widely discussed in linguistics and formal semantics, but their formal treatment in logic is surprisingly modest. In this article we present a sound, complete, and cut-free tableau calculus $${\textbf{TC}}_{R_{\lambda }}$$ TC R λ for the logic $${\textbf{L}}_{R_{\lambda }}$$ L R λ being a formalisation of a Russell-style theory of definite descriptions with the iota-operator used to construct definite descriptions, the lambda-operator forming predicate-abstracts, and definite descriptions as genuine terms with a restricted right of residence. We show that in this setting we are able to overcome problems typical of Russell’s original theory, such as scoping difficulties or undesired inconsistencies. We prove the Craig interpolation property for the proposed theory, which, through the Beth definability property, allows us to check whether an individual constant from a signature has a definite description-counterpart under a given theory.
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