Pseudo-Boolean valued prolog

A generalization of conventional Horn clause logic programming is proposed in which the space of truth values is a pseudo-Boolean or Heyting algebra, whose members may be thought of as evidences for propositions. A minimal model and an operational semantics is presented, and their equivalence is proved, thus generalizing the classic work of Van Emden and Kowalski.Research supported by PSC-CUNY Grants 666396, 667295 and NSF Grant CCR-8702307.     

Reasoning About Games

A mixture of propositional dynamic logic and epistemic logic that we call PDL + E is used to give a formalization of Artemov??s knowledge based reasoning approach to game theory, (KBR), [4, 5]. Epistemic states of players are represented explicitly and reasoned about formally. We give a detailed analysis of the Centipede game using both proof theoretic and semantic machinery. This helps make the case that PDL + E can be a useful basis for the logical investigation of game theory.     

Justification logics and hybrid logics

Hybrid logics internalize their own semantics. Members of the newer family of justification logics internalize their own proof methodology. It is an appealing goal to combine these two ideas into a single system, and in this paper we make a start. We present a hybrid/justification version of the modal logic T. We give a semantics, a proof theory, and prove a completeness theorem. In addition, we prove a Realization Theorem, something that plays a central role for justification logics generally. Since justification logics are newer and less well known than hybrid logics, we sketch their background, and give pointers to their range of applicability. We conclude with suggestions for future research. Indeed, the main goal of this paper is to encourage others to continue the investigation begun here.     

Cue usage in memory for location when orientation is fixed

In previous research, it was demonstrated that including one or three cues surrounding a circular field had no effect on spatial memory for dot locations when the field's orientation was fixed, but that there were very large effects when orientation varied across trials (Fitting, Wedell, & Allen, 2007). In four new experiments, we explored the use of external cues in the fixed orientation environment, using 0, 4, 8, or 24 cues and manipulating task difficulty. In Experiments 1-3, the angular bias data supported the use of four quadrant-based prototypes regardless of cue condition, but there were clear cue effects on radial prototype locations. Increasing the number of cues enhanced accuracy of spatial memory for targets closer to cues. In Experiment 4, we severely challenged memory by using multiple targets and a filled delay before estimation. Doing so demonstrated an effect of cues on the categorical structuring of memory. Collectively, findings indicate that when orientation is fixed, cues bolster fine-grain memory, but that they only alter the default categorical scheme when memory demands are high.     

How True It Is = Who Says It’s True

This is a largely expository paper in which the following simple idea is pursued. Take the truth value of a formula to be the set of agents that accept the formula as true. This means we work with an arbitrary (finite) Boolean algebra as the truth value space. When this is properly formalized, complete modal tableau systems exist, and there are natural versions of bisimulations that behave well from an algebraic point of view. There remain significant problems concerning the proper formalization, in this context, of natural language statements, particularly those involving negative knowledge and common knowledge. A case study is presented which brings these problems to the fore. None of the basic material presented here is new to this paper—all has appeared in several papers over many years, by the present author and by others. Much of the development in the literature is more general than here—we have confined things to the Boolean case for simplicity and clarity. Most proofs are omitted, but several of the examples are new. The main virtue of the present paper is its coherent presentation of a systematic point of view—identify the truth value of a formula with the set of those who say the formula is true.     

Tableaus for many-valued modal logic

We continue a series of papers on a family of many-valued modal logics, a family whose Kripke semantics involves many-valued accessibility relations. Earlier papers in the series presented a motivation in terms of a multiple-expert semantics. They also proved completeness of sequent calculus formulations for the logics, formulations using a cut rule in an essential way. In this paper a novel cut-free tableau formulation is presented, and its completeness is proved.Research partly supported by NSF Grant CCR-9104015.